When a unit you control moves into a battlefield controlled by an opponent and you ambush Nidalee, Cat Form, then your opponent returns both the only enemy unit and Nidalee to hand with Star-Crossed, and you then replay that same Nidalee to the battlefield, does the replayed Nidalee still draw a card from her win condition even though she didn't see an enemy unit when she entered?

Yes — the replayed Nidalee still draws.

Combat doesn't stop just because the defending side loses all its units; it runs on until players pass and the Resolution Step completes (FAQ #7863). So the combat is still the same one when you replay Nidalee, she's a unit present at that battlefield during it, and she gains the Attacker designation in the cleanup following her entry (Rule 464.2.c.3.a).

At Determine Combat Result, your side is the only player with units remaining, so you win and every unit you control at the battlefield inherits that result (Rule 466.3.a/c). Her ability only asks whether she "remains after combat" — it has no requirement that an enemy unit was there when she entered, so she triggers and draws 1. (The original Nidalee that was bounced doesn't draw, since she wasn't at the battlefield when the result was determined.)

The one thing that would change this: if the Combat Showdown had already closed and combat ended before you replayed her, she'd be entering after combat and wouldn't win anything.