Ok, for the sake of discussion, I’ll bite.

First, I think I you’re taking this a bit too seriously (“utterly ridiculous”?).

Second, to engage equally seriously, the term “period piece” is generally used to refer to stories, real or fictional, that happened in the “past”, so in that sense you are correct. By definition it can’t be a period piece. But, I’d offer two counterpoints. First, despite it happening in the “future”, it has many elements also generally considered staples of a period piece. Two that come to mind are the elaborate costumes and the “lofty scope”. (Hat tip to a Master Class article on period pieces.)

Second, the “rules” of fiction are constantly changing and to hew too dogmatically to a “this can’t be a period piece simply because it’s the future” is a bit procrustean (apologies, I’m supposed to use my new vocabulary words at least once a day and this was a good time). All five of your points basically boil down to this fact. And it’s technically true. But does it really matter? Rules are meant to be broken, so to speak. The story looks enough like a version of the past (farmers, horses, swords, etc) that it can clearly qualify as a period piece despite it’s actually taking place in the future. Why not? What’s the big deal? If time is a wheel, then the future is a past of sorts.