Yeah black has serious compensation in this line. Imo, it is very sufficient, I don't know what the engine says, but it looks like white has serious difficulties.
Glek Four Knights - Reversed Halloween Gambit

So, if the main refutation of the Halloween Gambit (1.e4 e5 2.Nf3 Nc6 3.Nc3 Nf6 4.Nxe5?!) involves ...Ne5-g6, is Black able to get away with meeting 1.e4 e5 2.Nf3 Nc6 3.Nc3 Nf6 4.g3 with 4...Nxe4(!?), now that White is commited to g2-g3, occupying the retreat square?
yep it is considered an improved version of the halloween gambit and is more sound unfortunately it is very rare to get the opportunity to play it.
and @randomemory stockfish evalutes this position as 0.5 pawns at depth 26 in favour of white and stockfish is often accused of exagerating advantages.

it also prevents the refutation black normally has to the halloween gambit with the ...Nc6 because g3 exposed his rook

This looks decent for Black.
But why would White want to play 4.g3 ? The bishop has already a diagonal. This seems to just lose time.

Halloween gambit or chigago gambit is fun in bullet and blitz games! You get good attacking changes.

This looks decent for Black.
But why would White want to play 4.g3 ? The bishop has already a diagonal. This seems to just lose time.
I guess its a question of taste
I guess that's rather a matter of playing ability. Why lose one move to get the bishop on an inferior square while creating weaknesses on the kingside ?

This looks decent for Black.
But why would White want to play 4.g3 ? The bishop has already a diagonal. This seems to just lose time.
I guess its a question of taste
I guess that's rather a matter of playing ability. Why lose one move to get the bishop on an inferior square while creating weaknesses on the kingside ?
I'm not sure myself, but I do know that GM Davies recommended it on his DVD "e4 for creative attackers", so it must have some merit.

I'm not sure myself, but I do know that GM Davies recommended it on his DVD "e4 for creative attackers", so it must have some merit.
The exact line 1.e4 e5 2.Nf3 Nc6 3.Nc3 Nf6 3.g3 ?
1.e4 e5 2.g3 impresses me a bit more.
So, if the main refutation of the Halloween Gambit (1.e4 e5 2.Nf3 Nc6 3.Nc3 Nf6 4.Nxe5?!) involves ...Ne5-g6, is Black able to get away with meeting 1.e4 e5 2.Nf3 Nc6 3.Nc3 Nf6 4.g3 with 4...Nxe4(!?), now that White is commited to g2-g3, occupying the retreat square?