In your example, white has not played as any human master would play the King's Gambit. The opening is a gambit, not an attempt to grab a pawn and hang on to it. White should play for quick development. Here's an example:
1. e4 e5 2. f4 f5 $6 3. exf5 Qh4+ (3... Qf6 4. Nc3 c6 5. d3 Bd6) 4. g3 Qf6 {On
the face of this, Black is in a bad way. He's down a pawn, his Q is on a bad
square, and White has easy development. White is playing a gambit. He
should continue in gambit style and develop his pieces rather than worry about
the pawn count.} 5. Nc3 $1 {This is only an example of how White may play the
game. This is hardly a definitive best line. But I believe it gives white a
clear edge.} (5. Qh5+ $6 Kd8 6. Qg5 $2 exf4 7. Qxf4 d5 8. Nc3 c6 9. d3 $2 Bd6
10. Qf2 Qxf5) 5... exf4 6. Qe2+ Kd8 7. d4 Bb4 8. Bxf4 Qxf5 9. O-O-O Bxc3 10.
bxc3 Nf6 11. Nf3 Re8 12. Ne5 Re7 (12... d6 $2 13. Nf7+ Kd7 14. Qc4) 13. Qd2 $1
(13. Qc4 d6 14. Bg2 Qe6 (14... dxe5 15. dxe5+ $18) 15. Qxe6 Rxe6 16. Nf7+ Ke8
17. Ng5 Re7 18. Rde1 Nc6 19. Ne4 Nxe4 20. Bxe4 h6 {And white has a clear
long-term advantage due to his Bishop pair and better development.}) 13... Qh5
14. g4 Qe8 $18 {One look at this position shows the poverty of Black's play.
Houdini only gives this a 1.01 advantage after 20 ply (I didn't waste any more
computer time on the position), but I think most humans would agree that white
is close to winning.} (14... Nxg4 15. Be2) *
I don' see any difficulty for Black to equalize. Reasonable play might be:
1.e4 e5 2.f4 f5! 3.exf5 Qh4ch 4.g3 Qf6 5.Nc3 exf4 6.Qe2ch Kd8 7.d4 fxg3 8.hxg3 Nc6 9.Be3 Bb4 10.Qd3 Bxc3ch 11.bxc3 Qf7 12.Bg5ch Nf6 13.Be2 h6 14.Bh4 d6 15.c4 Ne7 16.g4 h5=