When Bone Skewer targets Rockfall Path, what will happen to the unit played?

No — no unit gets played at all: Bone Skewer's instruction to play the chosen unit to Rockfall Path is simply negated, so the unit stays in your opponent's hand and nothing gets Stunned.

Bone Skewer choosing Rockfall Path is a legal choice (the battlefield is a legal target — a battlefield is only a targeting restriction when it appears that way, CR 355.10.b), but "They play that unit to that battlefield" can't be performed because Rockfall Path says units can't be played there. Per Rule 359.3.e.6 that instruction is Negated rather than Ignored, so Bone Skewer resolves doing nothing except revealing the hand (same principle as Temporal Breach at Rockfall Path, FAQ #11673). The Stun is a linked "If they do" instruction pointing at the play action, so it never fires — and the unit isn't on the board to be Stunned anyway.

Worth noting: if the Bone Skewer was played from face down at Rockfall Path, you're forced into this — Rule 811.1.d.5 makes you play the unit at the battlefield the spell was played from, so the whole spell whiffs (FAQ #13108). From hand, just pick a different battlefield.