I don’t understand why they didn’t just use an integer. You can’t have half a HP in AoE and nothing has HP so high that it would overflow a 32 bit integer. Seems like it would avoid a lot of problems.
They don't use floating points.
He didn't mention (IIRC) the possibility of rounding bugs; the reason he cited was something a bit more interesting: Floating points are not deterministic, which makes multiplayer challenging, as they simulate game state on each client's computers and only send commands across the wire.
One wonders if the "out of sync" errors that plagued Age of Empires in my youth were partially explained by FP determinism issues!