I can't quite pinpoint why YouTube doesn't have the same feeling though.
But YouTube has also completely destroyed their entire concept of having a "YouTube community" over the years. There might be something of various creator communities in various niches, but the heavy censorship, mess of a comments section that does everything in its power to halt any form of conversation, leaving only spam and idiots in most comment sections, etc. left it with nothing of a community, or any real creator/consumer dynamic.
YouTube no longer has private nor direct messages, so if people want to communicate they have to do it on another platform. It's also just a bit of a mess with the transition from the original idea of "everyone has an anonymous handle" to "every must have their Google+ profile linked and use their real name" to "Google+ is dead and now some people have silly handles and some people are real people." The whole thing adds up to make for a place with no coherent community.
Twitch chat is for emoting, especially in ways that please the streamer. Trying to actually chat with someone on an active Twitch channel is futile.