It is mate. Kxa7 is not a legal move because the king cannot move into check.
Questionable Checkmate
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No that's not a bug. That's checkmate, it doesn't matter that the bishop is pinned, the king cannot take a piece that is protected by another piece no matter the circumstance.
This issue has been raised before:
http://www.chess.com/forum/view/general/a-chess-rule
It's not a bug. The rules state that you cannot move your King into check, which is what you're doing if u play KxR.
Roger that. Thanks for the fast replies.
You can make sense of checkmates by imagining that the goal of the game is to be the first to capture the opponent's king. If you capture the opponent's king before he or she captures your king, then you win. Checkmate is where you have absolutely no choice but to let your king be captured in the next move. In this game, black has no choice but to allow his king to be captured in the next move. The black king taking the white rook would cause the bishop to capture the black king, and white wins. Moving the bishop would expose the white king, but that doesn't matter. The black king dies first, therefore white wins.
Hmmm, if we change it a little then the rook pinning the bishop is now pinned so it\s mate again 
AbelDean...your knowledge of chess is doubtful because of the words you put here to describe king capture...absolute non sense....
Of course there are no captures of the kings in chess. Moves that leave the king vulnerable are illegal, and the game ends before the king can be captured. But, the principle of checkmate is that the king WILL BE captured in the conceptual next move, supposing there could be a next move.
And that causes me to advocate a simpler version of the game that would be easier to learn: do away with the rule that makes it illegal to make a move that leaves your own king vulnerable, do away with checkmates, and instead make it the goal of the game just to capture your opponent's king first. There would be no more stalemates: only a loss when the losing king is trapped. And there would be no question among anyone that the OP game really is a losing game for black.
I know where the OP is coming from, Ive debated these types of situations myself. However, within the rules of chess this is definately mate and not a bug.
Let me explain carefully: whenever it is a checkmate, it doesn't mean the game is over, checkmate means that the other opponent is warning that ur king is going to die, so in fact, king kills the rook and the bishop kills the king and the game is over! But chess ends with a checkmate, they don't continue! For example:
This could just be my lack of knowledge of Chess, but it seems to me this should NOT be checkmate.
White's supporting Bishop is pinned by Black's Rook, thus Black's King should be able to capture White's Rook (in my understanding). I believe this to be a bug with the app.
Your thoughts?