>>>...but was she right to do it from Saturday Night Live's Live broadcast?
If SNL wants to not invite O'Connor back, or cut her from the rest of the show, or yank her off stage, yep it's their show, fair enough. Same with blizzard - they can stop the interview and tell him he doesn't get to say what he wants on their show. I wouldn't exactly be impressed with that, but in general it's their show, their rules.
To take his winnings and ban him from the game is absolute bullshit.
I'd like to play Devil's advocate with your argument, if you'd be interested and willing. Couldn't one say the same thing about Blizzard: "it's their game/tournament, their rules"? They banned him from participating in Hearthstone esports for 1 year. Is the primary distinction that O'Connor doesn't depend on SNL for her livelihood? Would the argument hold if O'Connor were employed by SNL?