In my occasional games with the BDG (usually via the move-order 1.e4 d5 2.d4) I always answered 2...dxe4 3.Nc3 e5 with 4.Nxe4 and never encountered a major problem.   I always thought that the main line after 4...exd4 was 5.Bb5+ c6 6.Qe2 as Lev gives above, but 5.Nf3 (which I've also played before) certainly looks very interesting and in some ways reminiscent of the Scotch Gambit (the pawn structure is much the same).

3...f5 was discussed in an earlier thread.  If I remember rightly White was able to obtain approximate equality by playing 4.Bg5 first, before f3, and then steering play into lines of the 4.f3 Staunton.  It's a pretty good line to try though as I guess most Whites will think it looks dubious but then be surprised at how hard it is to refute.

Now let's compare Gutman's with the line 5...Bg4 6.h3 Bh5 7.g4 Bg6 8.Ne5 e6 9.Bg5!? c6 10.Ng6 hg.

Black's bishop got to g6 in three moves (g4-h5-g6) instead of two (f5-g6) but White played h3+g4 instead of h4.

If White wants to castle long, he'll want to play a further h3-h4 to have Gutman's Rh3 on ...Bb4.
But then it turns out he spent a whole tempo on g4 which he could regret.

So this appears a clever way to avoid long castlings.