This line is usually mentioned in passing in books dealing with the Two Knights or the Scotch Gambit. All the ones I have recommend taking on c3 with the Knight, and suggest that Black is then comfortably better.
Bologan gives 6...Nxc3! 7.bxc3 d5! 8.Bb5 Be7 9.Nxd4 Bd7 as his main line and continues analysing for a few further moves, while Emms mentions additionally 9.Ne5 Bd7 10.Nxd7 Qxd7 11.cd a6 12.Ba4 b5 13.Bb3 Na5. Johnsen also recommends 6.Nxc3.
This approach is indeed kylemeister's old book recommendation.
HagenWatch1 wrote on 09/03/20 at 18:59:03:
I’d like to know why the GM who is showing off the Nakhmanson Gambit doesn’t mention this 6...Nxc3 line but only the 6...dxc3 move
I'd guess that's because 6...dxc3 leads to sharp sacrificial play where White gets the exciting game he wants. 6...Nxc3 keeps things rather dull and under control and give Black a better position without any pyrotechnics, which is not a very good advertisement for this line!
HagenWatch1 wrote on 09/03/20 at 18:59:03:
And interestingly enough the GM’s version of Stockfish is also choosing this 6...dxc3 line and not this “old book recommendation” of 6...Nxc3. Curious indeed.
Not really curious at all. My engine (Stockfish 12) also decides after a while that 6...dc is slightly better than both 6...Nxc3 and 6...Nd6, but 6...dc involves Black's king being dragged out of safety (to f6 in one line). If you're an engine, then that's what you should play. For a human player, though, it makes much more practical sense to play a quiet line that gives you an advantage in a sound position than it does to grab all the material that's on offer and then march your king into the open with all the risk that entails, even if the latter option is objectively slightly stronger.