Oh boy, this seems fun.  I'm probably gonna ramble on a bit, mind if I ramble on?  Alright then rambling time.
First off, the most notable thing about this list is that over half (5/8) is from Studio Ghibli.  A little disappointing, but not surprising in the slightest.  Ghibli is by far the most famous Japanese studio in the west (thanks in large part to Disney pushing it with their exclusive deal) and the most well-known family-audience studio in Japan. A lot of animation buffs say they're a bit overrated in the west, but they are popular for good reason, and their films probably do deserve the heavy presence.  Looking at them individually

Spirited Away - If you're gonna pick one film to represent Ghibli, this would be it.  I wouldn't say it's the best work from either the studio or Miyazaki, but it's definitely up there for both.  Massively popular and critically acclaimed in both Japan and the West, winner of numerous awards including an Oscar, etc.

Grave of the Fireflies - Another solid choice, it's possibly Takahata's best work and definitely his most famous.  Takahata was co-founder of Ghibli and part two of their dynamic directing duo, but unfortunately gets completely overshadowed by Miyazaki.  Infamous for being one of the most depressing movies you'll ever see; I'm pretty sure I just laid in bed and cried for an hour or two after watching it.

My Neighbor Totoro - A bit tricky.  As a character Totoro is definitely one of the most famous and influential anime figures both in the West and in Japan - if Ghibli is Japanese Disney, he's their Mickey Mouse.  But as for the movie itself I really don't know.  It's a good film, but it's definitely geared toward younger kids, and I think that those who saw it as a child will have much stronger feelings toward it than those who didn't.  If judging solely on the merits of the film itself there are several Ghibli films I'd definitely place above it, but if you go by the importance of the character it probably deserves a spot on the list.  On a fun side note its original theatrical release was a double-feature with Grave of the Fireflies; I can't imagine two films that are more polar opposites of each other.

Princess Mononoke - Now it's getting really tricky.  Mononoke is another great film, definitely on Ghibli's A list, but I wouldn't say it's any better or more notable than any other film on said list.  It's more popular in the West than the others, probably due to the fact it's more action-adventure than the rest - basically the studio's only PG-13 fare.  If this was a poll for a Japanese audience I would 100% replace it with either Nausicaa or Laputa, maybe even both; both have had a far greater cultural impact than Mononoke, and are probably better films to boot.  For the west though - I'd probably still consider replacing it if I was making said list, but I can't really argue against it either.

Howl's Moving Castle - The only film on this list, Ghibli or otherwise, that I 100% disagree with.  It's not terrible or anything, but it's easily in Ghibli's bottom-tier films and one of Miyazaki's personal worst works.  It (unfortunately?) has a pretty decent following in the West which if I had to guess is thanks mainly to nostalgia - it was made right after Spirited Away and so came out during the apex of the early-00s Ghibli Hype that followed its Oscar win.

Other Ghibli to consider - I already mentioned Nausicaa and Laputa; Kiki and Porco Rosso are also high on the A-list along with Mononoke.  If I had to pick just one from a critical standpoint my gut says I'd probably pick Laputa, but really it's a toss up overall.  If you want the most popular-in-the-west one it's probably Mononoke.  The Wind Rises and Princess Kaguya also have pretty decent critical acclaim, but I've yet to see either myself (been slacking on Ghibli movies the past few years or so).
Special mention for Whisper of the Heart.  It's not the most famous or well-known Ghibli film (though it is known simply by virtue of being Ghibli), but it is generally regarded as one of the studio's best works.  I mention it because it's my #1 favorite movie of all time, animated or otherwise, and if I could put any work into this list for personal reasons this would definitely be it.  The only movie made by Yoshifumi Kondo, who was expected to join Miyazaki and Takahata as the studio's #3 big director but died from overwork shortly after the film was released.

Now moving on to the other films

Akira - A no-brainer.  On a purely technical level Akira is considered one of the greatest masterpieces of Japanese animation, and perhaps of all animation in general.  The poster child of what Japan's bubble economy allowed the animation industry to accomplish.  The plot/characters/writing may be a bit on the iffy side (especially compared to the manga it's adapted from), but are still solid enough to make a good movie.  As an aside, if as a film buff you want a decent understanding/familiarity with Japanese animated film then this is 100% required viewing, though I'm a bit doubtful as to how much you'd actually enjoy it.

Your Name - Part of me wants to write this off as a 'flavor of the year' - it's still riding the hype from its original release a bit under two years ago - but honestly it probably is a solid and deserving choice. If this were a list of top 8 anime film directors then Makoto Shinkai would almost certainly deserve a spot, and Your Name is by far his best work (or at least most accessible, being the first he's made for a mass-appeal family audience).  Absolutely stunning animation and scenery (as with everything Shinkai does).  JJ Abrams is apparently producing a Hollywood live-action adaption??

Ghost in the Shell - Speaking of directors, another that definitely would belong on a 'best of' list is Mamoru Oishii, and Ghost in the Shell is easily the best show to represent him.  I have to admit I've yet to watch it myself but it is a very highly regarded film.

Continuing with directors, there are two big names conspicuously absent.

Mamoru Hosada - If Ghibli is Japanese Disney, this guy is Japanese Dreamworks.  A rising star over the past 10-15 years, he's established himself as one of the only mass-appeal family-oriented anime film directors who can consistently compete with Ghibli.  Unfortunately, while his body of work as a whole should definitely be ranked high up there, I can't think of any one show in particular that stands out as exceptional.  I'd love to see him represented somehow, but there's just no one film that deserves a spot on its own.

Satoshi Kon - Possibly the most famous anime film director after Miyazaki, especially in the West.  He sadly died quite suddenly in 2010 after making only four movies, but all four are very highly acclaimed both critically and popularly, in Japan and in the West.  Something of his definitely belongs on the list, though which one in particular I really can't say.  Perfect Blue, Millenium Actress and Paprika are all considered masterpieces in their own right and could easily fit on there.  (Tokyo Godfathers is also a fantastic film, but probably wouldn't fit on a 'best 8' list as well as the other three).  Another side note - in a situation very similar to Kimba the White Lion and The Lion King, many fans say that Hollywood has ripped off two of Kon's films - Black Swan from Perfect Blue, and Inception from Paprika.  There's some evidence to support this, but you mileage may vary.

There's tons of other films I'd love to bring up, great shows that anyone decently familiar with anime should know and that I wouldn't consider 'niche' but you probably would.  So I'll sadly leave them out.  The only other film I can think of that I would consider for such a list is Macross: Do You Remember Love?  Made in 1984, it was widely regarded as one of the best anime films for decades, and is still a major classic masterpiece.  The Macross franchise in general is huge in Japan - as a mecha series it's only a bit below Gundam in popularity and renown - but unfortunately thanks to licensing and copyright issues has never been released outside of Japan (Thanks Robotech).  Anyone who's decently knowledgeable of anime should know the film, and it's definitely required viewing for an anime film buff, but it'd probably be completely unknown to anyone else.
And of course I desperately want to recommend End of Evangelion as it really is a masterpiece and one of the most important anime films ever made (I've seen film buffs say it's one of the best movies they've ever seen) but it's inexorably tied together with the TV series, you can't have one without the other.  So that's sadly a no-go.

So uh yeah, there's my thoughts.  That rambling enough for you?  Lemme know what you think I guess.

And one last note regarding the rest of the tournament - I really don't think Pixar deserves an entire 1/4 of the slots to itself. Not that you couldn't easily pick enough great Pixar films to fill it out, but it really crowds out the 'everything else' category far too much.  I can easily think of three times as many films in 'everything else' that deserve to be in a 'best animated film' competition more than much of Pixar's library.  If I was making the lists and Pixar was rolled into a 16-slot group with 'everything else' I'd probably give them 3~5 of those slots.  Toy Story(2/3?), Wall-E and Up for sure, maybe 1~2 others.
And for 'everything else'  I sure hope you remember the very deserving old classics that should be fairly well known but often get overlooked.  Iron Giant, Secret of NIMH, Prince of Egypt, etc.