4.h3 e5! White is also in big trouble.

Not just attacking the knight, also mobilizing the remaining pieces to the kingside. There followed:

And the attack soon took its toll.

In order to seize the d6-square with the knight, even at the cost of the exchange.

Now White's control of the long diagonal adds to his compensation.

6...Nxa6 7.Nxf5! gxf5 8.Rxd8 Rxd8 9.Qe5 +-

Thanks to his strong passed pawn and the exposed black king, White is practically winning.

By tactical means Black nullifies the weak squares on d5 and e4.

Instead, 2.Qd1 was correct, when 2...Ne7 3.Be6 Bf4 4.g3 Rf6! 5.Bh3 Bh6 6.Qa1 Nc6 yields Black a slight advantage – Nataf. The desired ...d6-d5 is just one move away.
2.Bxe4? also failed to d5.