I think it's unfair to say it's anti-intellectual. I actually read the article and while i haven't played the game, it seemed fine, if not very limited in scope, which i think is more or less what people are taking issue with it, it would be my issue with it, since it really did only cover the story, with no comment on the gameplay. This sort of constricted review is pretty common, and it's a bit of a kneejerk reaction to condemn such a review for many people, myself included, though perhaps not be as prominent or hostile, but i do kinda roll my eyes at a review when it's clearly coming from someone with a political axe to grind.
I do think a lot of "progressives" and "intellectuals" more or less just create sacred topics for themselves that are free from criticism, which i think largely invalidates those self-appointed labels. If they can't criticize a game because it has a non-straight white cis male protagonist, than they don't get to call themselves intellectual.
I guess the point is that it's not anti-intellectualism, partly it's a defense of dumb games that there's no problem if they're dumb. It's also parly a defense of games who don't ground their appeal in political pandering, and i do mean pandering. You won't find many people harping on bioshock 1 for being preachy, even if a huge amount of the dialogue was pure political ideology by a severely political man, and i think there's at least 2 big reasons for that. Firstly, it was the game's own world, nor was is an overt representation of something in the real world, like the movie avatar was, just to provide an example. It explored general concepts, and it didn't point to real-world things. Secondly, it never really claimed the explored political philosophy was right or wrong. Rapture may have failed in the end, but it accomplished crazy things in that time. It can't be said to be purely wrong or right, purely good or evil, it had it's merit and it's flaws, and this is largely what made it so popular, but it didn't skimp on the game play to accomplish that, nor would a review of bioshock be complete without a nod to, what is in my opinion, a creative and viscerally fun take on the shooter with it's plasmids and variety of weapons and viable tactics.
It sort of feels like game reviewers are flocking more and more towards games with writing akin to a 5th-grade creative writing class, where the child author writes about how a character strikingly similar to themselves, with one character change in the name of their own name as the hero's name. they're a hero and the best person ever, and a villain is a classmate they dislike, and they're evil and disgusting and dumb. That's not intellectualism, and replacing the child with a political opinion being the hero doesn't make it any better. Simply including politics in something does not make it intellectual, nor above criticism, or even casual scorn. If these games don't even have gameplay to fall back on, (and don't get me wrong, i think a game can stand with just story and no real gameplay, but ONLY if that story is strong) then those reviewers that like it may be largely just giving it good reviews because it agrees with their political opinions, regardless of actual quality of story or gameplay, and i think lots of people, myself included, have gotten somewhat irritated at this practice over the years.