White is fine after f4 but Black is too and so Ne2 never caught on. It's tactically ok to play this way ( something like1.e4 e5 2.Ne2 Nf6 3.f4 ef 4.Nxf4 Nxe5 5.Qe2 Qe7 6.Nd5 Qe5 7.Nc3 c6 8.d4 Qxd4 9.Be3 Nxc3 10.Bg5+ is nasty) but Black has a few ways to get out of the opening without any trouble.
3.d4 is an idea of Stefan Bueker(?) but that's a real gambit and I really don't know much about that.
1.e4 e5 2.Ne2 Nc6 3.f4 Bc5! seems good.
White should just play 4.Nbc3 d6 to get a King's Gambit Declined, where White would clearly prefer his KN to be behind the f pawn. Instead 4.fxe5? d6! is quite bad for White...