1.d4 Nf6 2.g4
It's also known as the Bronstein Gambit (A45) or Bullfrog Gambit. The opening moves are 1.d4 Nf6 2.g4! The move 2.g4 tends to disrupt black's normal development. For example: if black declines the gambit with 2...d5 then 3.g5 can be very troublesome. In some lines white gets play on the half open g-file with Rg1. If black captures the g-pawn with 2...Nxg4 white picks up 2 tempi and a long lasting strategic attack. Like most other gambits white gets good control of the centre and a good development of his pieces. Black may have to defend throughout most of the game.
The complete text of the analysis of the game:
1.d4 Nf6 2.g4
Gibbins-Weidenhagen Gambit (A45).
Personally I think, if you want to prove that 2.g4 is wrong, than accept the gambit by playing 2...Nxg4. Now black is trying to prevent g4-g5, but 2...h6 doesn't stop this move. An interesting line is the Oshima Variation: 2...e5; black gambits his e5 pawn to get development and counterplay.
A developing move and controling the centre. Defending the g4-pawn with 3.e3 or 3.h3 is too pasive. Why bother defending it, as you were giving it away on the second move.
Black could accept the gambit by playing 3...Nxg4, but then his second move becomes rather weird.
If black doesn't take the g4-pawn, white will push this pawn forward eventually.
An alternative is 4...Ne4 5.Nxe4 dxe4 6.gxh6 gxh6 7.Bf4 Nc6 8.e3 and white is slightly better.
An alternative is 5...Bf5 or perhaps 5...Ne4.
Rather passive, perhaps better is 6...Bb4.
Alternative moves are 7.Nf3 or 7.0-0-0.
A strange move. Better was to develop the pieces on the queenside.
Better is 8.Bxe7 Qxe7 9.Qf4 Nf6 10.0-0-0 and white is better.
Again a strange move with the Knight. Perhaps better is 8...Nc6 9.Qf4 f5 10.Nb5 Bd6 11.Bxd8 Bxf4 12.Bxc7 Nxd4 13.Nxf4 Nxb5 14.Nf3 and white is better.
9.0-0-0 Nf5 10.Nf3
At this point white is fully developed; black's queenside is untouched.
Not good. Better is 10...Nc6 11.Rde1 b6 12.e4 dxe4 13.Rxe4 Bb7 14.d5 Bxg5 15.Nxg5 Nce7 16.Re5 and white is better.
An alternative is 12.Qf4 Qd6 13.Ne5 f6 14.e4 dxe4 15.Nxe4 Qf8 16.Ng4 and white is clearly better.
Better is 12...f6 13.e4 fxe5 14.exf5 exd4 15.Nb5 c6 16.Nxd4 e5 17.Rde1 and white is better.
An alternative is 13.e4.
Developing the queenside (and protecting the c7-square), but it's too late. Perhaps 13...Nd7 is better.
Ofcourse 14.e4 dxe4 15.Bxe4 Nd6 16.Rde1 Nxe4 17.Nxe4 Bd7 18.d5 is perhaps better, but I liked this sacrifice.
Possible continuations are:
15...Rf8 16.e4 Nb4 17.Bxf7+ Rxf7 18.Nxf7 Nxa2+ 19.Kb1 Qxf7 20.exf5 Bxf5 21.Qe5+ Kd7 22.Qb5+ Kd6 23.Qxb7 Re8 24.d5
15...Nd6 16.g6 Rf8 17.gxf7 Nxf7 18.Ng6 Nh6 19.Nxf8 Qxf8 20.Qe4+ Qe7 21.Qg6+ Kd8 22.Rdg1 Nb4 23.Qxg7 Nxd5 24.Rxh6.
Both times white will win the game.
A perfect example what the Gibbins-Weidenhagen Gambit (Bullfrog Gambit) can achive.
Perhaps not always pretty, but it can be effective.