The issue isn't people being defensive Because Games, it's that there is a massive gulf between games that can be classified as purely commercial and games that can be classified as purely artistic. Just because you can point to games like Call of Duty or Gone Home that fit very neatly into one category, that doesn't change the fact that many games, maybe even most games, especially on itch.io, are an awkward fit for either.
Where would you class Hyper Light Drifter? Or Pillars of Eternity? Or Dark Souls? Or Monument Valley? Where would you class something like a basic flash game, where there's no serious artistic intent, but no possibility of making money? Is there anything coherent in calling Mystery of Time and Space a commercial game?
I get that sometimes you're really just looking for games with serious artistic intent, or games that are mindless time-wasters, but what you're proposing is that somehow all games be categorized into a binary classification that immediately forecloses on any room for nuance.