Actually, black has a counter threat of Qg1# so if 1. Rxg7 then black will follow up with 1...Qg1# so you must be careful to watch your opponents threats also 
That is why white must sacrifice the queen with check so that black does not have time to execute his own mating threat.
Chess mentor problem 0026130
Rxg7 is also mate in 2... only it is ambiguous. All posible moves on the board lead to mate the next move or mate the move after that. And none of them inolve losing a queen for mate, not that that is the most important thing of course, as mate is. However mate is still the same number of moves away with the threat of mate immediately.