Your definition supports my original post. Certainly, games are made through the application of human creative skill and imagination, among a litany of other skills necessary to get games to function. But, as I said, most games are not made for the sake of art (that is, for the sake of being appreciated primarily for their beauty of emotional power), and without that purpose, it is not art, it only a product. That doesn't mean that the developers don't love their games and want people to enjoy them, or anything of the sort. But to most developers, when they worry about whether a player will enjoy their games, it's in the sense of, "Can they get immersed through the presentation and the mechanics? Are the mechanics fun? Do they remain fun for a second playthrough?" They're absolutely passionate about games because, as you say, they wouldn't work in such an atrocious industry if they didn't. But passion doesn't make something art. It just means that it's a product with love put into it.
You mention art IN games, but such as Mario's music. But Mario's music is not the same AS the game. But I said this as well, that art is made for games.
Mind you, if, for whatever reason, something like Shenmue 3 were to get censored, I'd be pissed, because Shenmue 3, like the prior games, is art. That desire for players to appreciate the games for their beauty and emotional power is central to Yu-san's ideas for the games, and he accomplishes the goals of making Shenmue both beautiful and emotionally powerful.
I think Duck said it best by pointing out that games are an art form. That games are capable of being art is commendable, but I think it's quite the disservice to those games that actually manage to be art to be lumped in with an Assassin's Creed or a CoD or worse, some game sloppily slapped together with Unity assets and inadequate code that barely works. Let the games that strive for and achieve art to be appreciated for how unique and rare they are. There's nothing to be gained by saying that all games are art, only the dilution of the idea of art itself.