There are many facets to video games, but boiled down, they’re a series of actions that tell stories. When I say Borderlands 2 isn’t a comedy, I mean exactly that: it is a very capable, if old fashioned, first person shooter with RPG mechanics. It slaps a hundred internet memes, slapstick jokes, and absurd narrative beats onto this to distract you, to convince you it’s a comedy video game. But don’t be fooled: it’s a funny shooter, but no comedy. It’s skinned a funny guy, and it’s wearing him as a suit, but that doesn’t make the product a comedy.
Auxier makes a useful point in observing that when categorizing video games, it's necessary to distinguish between the narrative architecture and the gameplay mechanics. Slapping a brightly-colored cell-shaded skin on an otherwise conventional first person shooter doesn't necessarily make it a comedy.
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Games are defined by their verbs. Borderlands 2 is a shoot, loot, and level sort of game: you shoot enemies, loot guns, and level yourself up. None of these are funny verbs. They’re all deadly serious. Tokyo Jungle, meanwhile, has you eating, marking, mating, and dying. These are comedic verbs in part because of their rarity, and in part because of how much they defy video game logic.
While it's hard to argue with the assertion that Borderlands 2 is best described as "a funny action movie," and I think that it's exactly right that "eating, marking, [and] mating" are "comedy verbs," the fact that they are comedy verbs doesn't actually have anything to do with rarity or "defying video game logic."
Auxier seems to be arguing that for a video game to be a comedy, it's not enough for the game to tell jokes; its gameplay also has to subvert player expectations. Against this assertion, I'd consider a game like Portal 2, which is not only incredibly funny, but also is built upon a basic subversion of a first person shooter engine. At the same time, I'm not sure that the comedy label fits Portal 2 any better than Borderlands 2. Portal 2's narrative is built on funny, absurd characters (like Cave Johnson), and probably the single best comedic voice performance any video game (Stephen Merchant's brilliant turn as Wheatley). At the same time, the game's story hinges as much on science fiction and thriller tropes as it is on making the player laugh.
Classic narrative definitions of comedy have as much to do with subject matter -- family, social mores, and etiquette -- and the focus and scale of the conflict -- the domestic individual and the preservation (however ridiculous) of the status quo -- rather than the architecture of the medium. If that's the case, then the big question isn't whether a game needs to subvert its gameplay in order to be a comedy, but why games which really fit the definition of comedy, such as The Sims or Catherine, are so comparatively rare.