I think that there would be no meaningful uproar if Blizzard would simply not host or broadcast that interview because they don't like it for whatever reason, and left it at that.
Exactly. It'd be like cloudflare kicking daily stormer off, but not before setting their DNS to resolve to 127.0.0.1 with a ttl of 1 year.
It was a post-game interview on a Blizzard event in a Blizzard broadcast. How is that different from "a private company not wanting to host <content>" ? The player had supported HK freedom on his Twitter in the past, yet was allowed to play in the tournament. Gaming events have not been places for sharing political ideas, like social media is.