Is 2 really that severe? To me, the position looks terrible with those 2 isolated pawns and the knights on relatively open field. At least white is going to be forced to make a move to stop 4... Rd1#, but that shouldn't be much a problem.
P.S. Rxd6 is great though, since black goes from 3 behind to 2 ahead.
a pawn itself can be decisive. Unless white plays terribly, it should be smooth sailing from here.
It is odd however that a book says mate in 2 when it can be stopped
Maybe it's from a real game. It's not a puzzle book.
Yep, your line prevents mate. The point of the book still stands though, since Black is definitely dead lost here. I'd probably go 3.Qd6 Kf7 4.Qxc6. Your idea with 2...Rxd7 is interesting actually, but after 3.Qxb8+ Rd8 4.Qxd8+ Nxd8 5.a4 for example, White has a winning endgame. Even better after 2...Rxd7 is probably just 3.h4 though, and Black's pieces will struggle to coordinate, eg. 3...Na6 4.Qe5 exposes how weak Black's pawns are.
The book I'm reading presents this as a quick mate.
1. Rxd6! Qxd6, 2. Qxg7#
or
1... Qe7, 2. Rxd8+ Qxd8, 3. Qxg7#
Well, here is an alternative that stops the mate.
2... Rxd6 is another possibility since it threatens mate and the knight is still defended since 3. Qxb8+ is answered by Rd8, which forces Qxd8 since there is no other move that white can do to stop mate or loss of their queen.