Continuation for white in the Bishops opening variation: 1.e4 e5 2. Bc4 Nf6 3. d4 exd4 4. Nf3 Nxe4 5. Qxd4 Nf6 I am currently reading Chess Openings: Theory and Practice - I.A Horowitz. The first opening displayed in the book is a variation of the bishops opening: 1. e4 e5 2. Bc4 Nf6 3. d4 exd4 4. Nf3. Seemingly the best continuation for black, if they can defend properly, is to continue 4 ... Nxe4 and to 5. Qxd4 respond with 5 ... Nf6.
From this point Horowitz goes on to consider the variation 6. Bg5 Be7 7. Nc3 c6:
rnbqk2r/pp1pbppp/2p2n2/6B1/2BQ4/2N2N2/PPP2PPP/R3K2R w KQkq - 0 8

This seems fine for white (to me) by basic chess principles (good development, castling around the corner). However I have two questions:

What if black had responded with 6 ... Qe7+?
It seems like white either trade queens and is worse or moves the king allowing Nc6 and is just worse?


What can white do after 5 ... Nf6? My thinking is that 6. Bg5 is the mistake so perhaps 6. Nc3.
Using Caissabase or the lichess masters database we can see that instead of Nxe4, Nc6 is more popular to avoid this gambit idea (the Urusov gambit) which is.... dubious but not so simple and seemingly scores fine enough. White has additionally scored p decently.
Qe7+ has only been played in one game, but seems good (black won that game, and SF12 gives -0.89 at depth 37, which is quite good). Nc6 and Be7 are both fine, but Nc6 is probably slightly better, judging from the fact that the lichess database shows it as most common with quite a hefty advantage for black, as opposed to the noticeably higher win rate for white (seemingly due to this very variation, as it turns out!). SF also likes Nc6 best, with an evaluation of -0.86 at depth 40.
After Nf6, Nc3 is seemingly more popular nowadays (as the lichess masters database), but has worse results.
My recommendation would be to consider not playing this gambit in the first place, since the Urusov Gambit is somewhat iffy, although it's probably still playable at a sub-master level, or to get a more recent book on this. This book is from the 1960s, as @Scounged very nicely pointed out, and as such is almost entirely useless- the only cases where it's useful are for general plans and opening names, and even here it will be severely lacking. If you want a starting opening book, Fundamental Chess Openings by Paul van der Sterren is great, although again note that many of the lines will be incorrect (esp in theoretical openings e.g. e4 e5 or the Sicilian)- focus instead on plans and names, and supplement with other sources (books, videos, courses).