Hangout exists because not everyone can join the IRC chat room or the discord (as myself). Hangout is mostly to talk with other people about random opinions or thoughts that players have, and while you are totally right, in the fact that this could be done in a chat room, by doing it in SRB2 servers it opens more interaction with each other (literally just playing together). One thing about hangout is that there are specially built maps (hangout maps) which tend to have mechanisms and scenery that helps making the experience better.
Hangout mustn't be misunderstood as roleplay, since in hangout, you usually give your own opinions or ideas, not acted ones. However there's no rule that says that you can't roleplay and hangout at the same time.
Basically Hangout is a more interactive chat room, that has more possible activities to interact with other players rather than just typing or playing level after level in co-op. Or battle after battle.