Alright, let me try to shine a light here, since most people reading seem confused as to who this guy is, or why it's a talking point at all.
I'm not a huge streaming fan, but the internet circles I frequent are a little closer to this corner of the net, so I am fairly well informed as to why this is a "big deal".
So to explain Dr Disrespect to you all, he is basically a charicature of the typical First Person Shooter, Battle Royale type of gamer. Tie in a little 80s aesthetic and a comedic backstory as "Two time Blockbuster world gaming champion" and you have a pretty decent recipe for success on twitch. Viewers tend to tune in to his streams because A) He is a highly skilled player, so they get to watch top end gameplay and B) he is a comedic charicature that pokes fun at this more "macho" scene in gaming, particularly around the battle royale games.
So why is his ban a big deal? Chiefly, because he has a very high profile. As one of the early successful streamers, he has become a symbol of sorts for the whole medium, and previous controversies (including filming in a public bathroom) around him have shone a bad light on the scene as a whole.
So why is the ban strange? Twitch does not show much restraint with the banhammer - their ToS is airtight and bans a LOT of types of content outright. Twitch has given many permabans out to both big and small streamers, for a range of reasons. Some people are banned for using racial slurs or hate speech, some for inciting violence or stuff like doxing against others. Some have been banned even for accidentally, or being tricked into, showing a few frames of pornography live on stream.
What's weird about Doc's ban is that Twitch haven't given a reason as to why they banned him. Twitch are usually very clear about this, and with a ban on a streamer with this kind of popularity, it's very odd that no statement has come out on why he was banned.
Internet being internet, speculation abounds. Some believe this is all down to a contract dispute - Doc reportedly recently signed a multi-million dollar deal to continue streaming with Twitch, which may have included certain stipulations such as "you must stream for 100hrs in x days" or whatever.
Some think this may have something to do with his recent endorsements of some pseudo science theories, as he has been talking about certain rocks he has bought that do something with bad energy, or whatever, and with his viewers largely being of a younger age, some think this is something Twitch wouldn't want one of their most well known streamers doing.
Some think its a response to a secret plan Doc and several other high profile streamers had to break away from Twitch and start their own platform.
All of these theories have reasons why they are unlikely to be true, but the main point here is that it's WEIRD that no statement was given, and that's lead to all this wild speculation which, considering some of the controversies and odd behaviour of the man in question, easily gets out of hand.
There you have it, a basic crash course in why this is a thing anyone is talking about at all. Probably time to get used to this sort of stuff, as among the kiddies, some of these streamers are like, rockstar famous, with the money to back it up.