Hi, I heard you chatted at one of the Korean Rust stream with chechekun XD. I'm chechekun's friend and let me answer the questions you had. (mind you, i'm just another viewer on that stream, not an actual stream affiliate)
As for the rules in channel goes, most Korean streams ban non-Korean chat because most people aren't fluent enough to have conversation/interaction in another language, and because they're decently big streamers (with usually 2k+ viewers), it doesn't really make sense for them to allow multiple languages. So sorry about that.
For the tagging wise, this is common for most Korean streams also, but Koreans have a tendency to form a sub-community amongst viewers and they usually end up being harmful/toxic to the stream in general. so to prevent that and cut the source, streamers don't allow tagging (@)  at all--which I recommend DM'ing in the first place if you find it necessary.
As for why Rust got so boosted recently, one of the big streamers, J1NU (https://www.twitch.tv/jinu6734), got a private server of Rust (costing around 1k USD equivalent according to rumors) and got like 30+ other streamer to join him on a massive-scale joint stream where everyone streams from their own perspective. and TaemTaemBuRin (https://www.twitch.tv/2chamcham2) is one of the members.

They are not any regular RUST streamers or anything, but they are considered what's called "variety-game streamers," where they just jump around playing different games now and then, so the audience is more based off of persona of each streamers and the talk-show radio content that they provide alongside with the games, rather than the focus on the gameplay itself--hence RUST being some "one-time" thing for them. In fact, although J1NU is considered pretty decent at gameplays, TaemTaemBuRin explicitly states on her introduction that she's bad at every single game that she plays. XD I guess this persona-based fandom in Korea is different from game-based fandom that you see in English streams.

Anyways, I hope this answered most of your questions. From what I can tell though, it seems like you have quite an interest in RUST and that's why you wandered into Korean streamers, but I'm sorry to tell you that you're probably not gonna see them play this game after 2 weeks at best (or even a week from now). I don't know much about the game itself, but from what I can tell, you need quite a bit of investment in time for this survival-genre, and although there may be some gamers who enjoy this game, most stream-viewers (who are different from gamers imo) are generally not interested in this kind of genre, so I don't think it's gonna last that long.
Anyways, if you have any more questions, feel free to ask me here on DM.