When an opponent casts Gust on your Irresistible Faefolk after you move it to the battlefield and trigger its ability to move Fizz in, does Fizz still get moved to the battlefield if Gust resolves first and bounces your Faefolk?

Yes. Fizz still gets moved.

Irresistible Faefolk's trigger ("When I move to a battlefield...") goes on the chain when it arrives, and it locks in the reference to "that battlefield" at that moment (Rule 359.3.f.3). Gust resolving first and bouncing the Faefolk to hand doesn't invalidate the trigger — the ability remains on the chain and resolves normally, moving an enemy unit (Fizz) to the battlefield Faefolk originally moved to (FAQ #11094).

Note that Gust targets a unit at a battlefield with 3 Might or less, and Fizz, Trickster has 3 Might — so your opponent could also have Gusted Fizz directly instead. But Gusting the Faefolk alone doesn't stop the move.