If a unit moves from combat before the showdown or damage, does the defender score a point for that combat?

It depends on whether the defender already controlled that battlefield — a combat win doesn't itself score a point; points come from Conquer or Hold (Rule 471). The defender is by definition already controlling the contested battlefield, so them winning the combat doesn't Conquer anything and they score nothing for it; they'd only bank that battlefield as a Hold in their next Beginning Phase if they still hold it.

Timing changes what happens to the combat, not the scoring. If the attacking unit leaves before a Combat Showdown ever opens, the combat simply ceases to be staged (Rule 323.9) and the Contested status clears in the following cleanup (Rule 323.10) — no combat happens, no one wins, no point. If it leaves after combat has opened, the combat still runs through the Resolution Step and the defender is the only player with units there, so they win it (Rule 468.3.a) and "when you win a combat" abilities trigger — still no point.

The one case where the defender does score: they weren't controlling that battlefield (e.g. it was uncontrolled or theirs was lost earlier). Then winning the combat and establishing control is a Conquer under Rule 468.5.d, worth a point if they haven't already scored that battlefield this turn.