The term that’s stuck for this subgenre (for better or worse) is “Character Action”. It’s not particularly descriptive - I agree with Kamiya in that it ought to make clear that it’s in reference to the Japanese school of action game design, which is very distinct from western sensibilities.

That said, I’d consider the best western take on the genre is the indie game Furi.

You know that Kamiya is the creator of DMC and a founder of PlatinumGames, right?