As you say, who cares if he liked it or not- but by that same vein of thought, who cares if random people didn't like his criticism? If you're here saying you think it's fine that he criticized the game, whether he's right or wrong about it- I agree, anyone can critique the game whether they've played it or not.
But, if you're also going to turn around and say the opposite, that other people shouldn't be allowed to then criticize him or his criticism? Why the double standard. He is just as open to getting criticized as he is for giving it. People have the same right to be offended and bash him on twitter as he does to bash them on twitter/twitch. He doesn't have to like the game, he can boost and skip the story then whine about it if he wants, he can brag about being a top notch player then stand in mechanics and die then blame healers for his own awful skill level if he wants... and other players can call him out for it if they want.
He's a professional (afaik he makes money to do this, making him a professional), part of his 'job' is playing/critiquing games in public- in turn, he's open to critique himself, especially when he acts like he's a god then can't figure out utterly mundane things like 'if I take more damage than my max health, maybe I should not trash the healers'. If he posts on twitter and has some really bad takes- why would people not respond to his terrible takes by calling them out? It's really obnoxious seeing people defend guys that act like he does and saying they just shouldn't get any pushback because it's ok to have an opinion as a streamer- you've every right to be as wrong as you want on the internet, and everyone else has that same right to tell you so.
His opinions aren't any more sacred or protected than those of the people against them.
As for twitter- this is the FFXIV forums, not twitter- people here aren't the ones responding to him on twitter, they can't control what happens on twitter, and many of us don't use twitter. As far as I've seen- most people on the forums are calling him out for things he did, I don't really see a problem with that. I'd rather have that then a community that bows to streamer whims because they huff and complain about gatekeeping every time their bad takes aren't treated like gospel.