Does Cull the Weak choose targets on play or on resolve?

On resolve — Cull the Weak never targets.

Its text is "Each player kills one of their units," which falls under Rule 355.10.e: choices made by each player as the spell resolves don't target. So no choices are made when you finalize it on the chain, and nothing is locked in at play.

When it resolves, each player independently picks one of their own units to kill (do as much as you can — if you have no units, you just don't kill one). Since it doesn't target, it can't be Deflected or countered by effects that require targeting.