That is not King's Gambit, but great game.
Hyper agressive game! (great ending combo!)

If Black had been a little less compliant (why not just take the pawn with 16...hxg6?) you'd simply have been an exchange behind in a lost position.
Right before the end, you're still dead lost -- 24...Qe1+ 25.Rxe1 (25.Nf1 Qxa1 is better but also lost) Rxe1+ 26.Nf1 Rxf1#. His 24...Qf2?? was a blunder that allowed you to check mate him.

Well, you sure talk up your games nicely!
I am not going to provide analysis because, well, you didn't ask for it. However, there is some confusion that I will try to clear up.
A gambit is when a pawn is offered in the opening for a positional gain or a lead in development. That is why 1.e4 and 2.f4 is a gambit when 1...e5 is played. However, these moves do not define an opening as the King's gambit for any first move for black. The opening is defined by the choices of moves from both sides. For instance, if black plays the Sicilian (1...c5), then 2.f4 is simply the 'Grand Prix Attack' line of the Sicilian.
Also, a combination involves a sacrifice to break through a defense. If your opponent simply blunders into a simple forced mate, I don't think we can really call it a combination.
Yes, I was confusing this game with another when I posted it - as you can see I made no annotations - I realized after, but have been too lazy to edit the post as of yet.
If you check out some of my other posts, you'll see very clearly that I do know what the King's gambit is, of course. I remembered doing the same first moves as a KG game, but of course my oponent played otherwise.
Thanks for the feedback though guys, it's helpful.
This was one very aggressive battle, as is typical of the King's Gambit game.
If the intense action through and through was not enough, the 7 move combo-knockout at the finish is certainly worth it!! With sacrifices, risky king-exposed positions, and a myriad of tactical plays, this game earns its title, and is worth a good look - check it out!