I agree with both your statement about AI training and Sweeney. However, I do believe there is a legitimate argument for using generative AI in game development, and I therefore also think Sweeney has a legitimate point, even if he's doing it as a reaction to Steam.

Something oft acknowledged as okay in art (or any creative endeavor) is inspiration. Legally, we can really go even further, saying that copying is okay as long as the thing being copied is sufficiently transformed into something that can be considered new. Say, for example, different artists' versions of a character such as Pikachu. We might be able to recognize them all as Pikachu, but also acknowledge that they're all unique and obviously the creation of one particular artist.

Why is this process a problem when it's done with technology? I, as a human, didn't get permission from someone else to transform their work. It's okay when I do it, but not when it's done algorithmically? Why?

I think this is a legitimate question that has valid arguments either way, but it's a question that needs to be answered, and I don't think a blanket response of "it's bad because it's stealing other people's work" is appropriate. If the model is very bad and clearly spits out exact replicas of the inputs, that's obviously a bad thing, just as it would be equally bad if I traced someone else's work. But what about the models that don't do that, and spit out unique works never seen before? Not all models are equal in this sense.