So, how it plays:
In The Last Federation, you control one individual ship. It's a powerful ship, far more advanced than any other ships but not invincible. From this vessel, you try to establish some sort of Federation. The game is parts Grand Strategy and Part Turn Based Shoot'em up.

The first part is the sector map. Here you can see the different races and what they're doing. Those races are basically playing a 4X Game of their own and it's entirely possible to spend the whole game just watching what they do. In time, they will enter alliances of their own, wage war with each other, research technology, send spies, everything your average 4X Player does within a game. Even maybe coming to a peaceful solution. The latter being quite improbable since each of the races are quite diverse in how they act, react and are governed.
Now, the player is basically playing a god game of sorts. The endgoal is the establishment of the Federation but the way there is up to the player. The player can influence the races in minor and major ways by completing missions, doing or calling favors, helping with research and construction or improving or destabilizing diplomatic relationships. These things cost money and time which you can earn through various means. Some of those missions involve combat of sorts, in which case you enter the technical map. Here you're sending your super powerful ship against entire armadas and try to complete varied objectives. The options of what you can do go quite deep. I'll give a bit of an AAR to better explain this:

I've got a bit of a Thoraxian Problen on my map. An expansionist race of aliens that is immune to most forms of influence and really, really hate me. I may have continously raided them for technology at some point, so I'm not too surprised by them wishfully calling their kids DEATH OF PLAYER. All of them. They're a hivemind. The problem is, while they hated me, they also hated just about everyone else, but the plushie parts of the solar system wanted to go the diplomatic route. Can't we just talk about it, they think and argue. I'll have none of that.
First order of business is convincing the Boarines to go to war. I could slowly change their policy over time, spending many ressources and watching the Thoraxians further spiral out of control or... killing their regent usually means they declade war upon the race they like the least. Hey, what do you know, with a bit of prodding they realize that Thoraxians stink. And with a bit of assassination (They now don't like me anymore), their new regent declares war upon the Thoraxians. That's one. Next one on the list are the Skylaxians. They don't like me (gosh, what did I do...), so I gift them tons of technology until they like me. Just enough to convince them to enter an alliance with the Boarines. This might actually be a first step towards a federation. Great, the Skylaxians are now at war with the Thoraxians. The Burlusts, meh I just pound my chest a bit, show them my large... guns and they're all over war anyways. They happily declare war with minimal coercion and maximum application of force. Some other races are a bit appaled by my brutality though.
So with three races in an all out war with the Thoraxians, I decide it's time to go. I swoop in with my battleship, take out defense armadas, capture outposts and factories and bombard their mainplanet. The three other races join in and to top it off, I assassinate the Thoraxian leader. This is going well. The Thoraxians aren't a problem anymore. Except... wait, the others are now in a threeway alliance and they all hate me. Except for the Burlusts. They like how I'm selling slaves to make cash and kill indiscriminately. Everyone else hates me too and I'm further from my goal than ever. Ugh. Do I knit the relations or do I set up an actual Federation with the remaining races? I could try my luck with the Evuk but they really, really, really hate my guts. Well only if I mess with their politics. Which I need to do to fix this. Oh well, no one said a Federation is easy pickings.

The game is filled to the brim with these decisions and moments and I can see it spawning similar stories to Crusader Kings. You could record what's happening and write a thrilling science fiction novel full of political intrigue and military decisions. To me, The Last Federation is a hit, quite worthy of being placed next to AI War.