PSA: Gambit games count as PvP matches for certain things. (Destiny)
I still had the 5th step of Nascent Dawn in my inventory, which requires 3 PvP match completions. The two Gambit rounds I just played progressed that to 2/3.
I suspect that anything that calls for "PvP" rather than "Crucible" specifically will let Gambit fulfill that requirement.