Okay, got it. I wouldn't call that PoS, but I see what you mean.

I think of the crux of PoS as the incentive system that keeps bad actors out -- if you act maliciously, you lose your stake.

It seems disingenuous to refer to that as proof-of-stake.

Errr, no. That's leader election, and is not a consensus algorithm by itself. It's part of the algorithm, which is nothing like PoS at all. That's like saying UDP and TCP are the same because they send packets.