Yes, after 2...g6 black is only a bishop behind and not immediately checkmated.
But that doesn't matter much for the result -- being a full piece behind is also enough to resign. And, that he stays a piece behind is immediately obvious -- white takes a bishop, black doesn't take back. So that doesn't really need to be explained.
On the other hand, what happens after 2...Nxe7 (or 2...Rxe7 for that matter) is not as obvious, so it's pointed out.
This is related to the concept of critical moves. To decide whether some move is good, there are some things that are important to look at more deeply and some things that aren't (2...g6 doesn't need further calculation, it's obvious that white wins). In a sense the question whether the initial position is winning depends more on whether 2...Nxe7 wins than on whether 2...g6 wins, even if the position after 2...g6 isn't quite as immediately lost as after 2...Nxe7.
2...Nxe7 is a critical move in a sense 2...g6 is not.