I think this is more of a current iteration of BR. I would say BR is a little more generic than this. My idea of it, which might not be exactly right I will admit, is just this: A battle royale game is last-man-standing or winner-take-all. The looting, houses, starting gear -- this all seems like variation more than essential.

It seems like what you're describing is definitely the mainstream take on the genre right now, but I think you could make another variant that isn't like the popular ones today but is still a BR.

Fair enough, I guess it's subjective what the actual minimum requirement is but I kind of agree with the Wikipedia article personally: https://en.m.wikipedia.org/wiki/Battle_royale_game

Reasonable.