I guess that's mate?

I know a player who wants to resign says I resign or tips his king, but I had an opponent who did neither but looked at me and said after I moved what appeared to be a mating move -- he said "I guess that's mate." I knew that it wasn't and that he had one blocking move. I felt it wasn't my job to point it out to him and just said "I guess so. Thanks for the game" So, I accepted the win without an official resignation.  Anything in the rules on this?

I think if he shakes hands and leaves after that, it is an official resignation.

Maybe you had mate in a couple more moves, and by saying what he said, he was implying resignation, and meant it would be mate in 3 or whatever, not that there was immediate mate on the board.

However, if he did believe checkmate was on the board and "concedes to checkmate", he loses even if it's not mate.

When I was 10, I actually lost a game in a class tournament that way. At the time I was probably the worst player in the class, and every time I played I was very unconfident. In that game, after only a few moves, my opponent moved his rook to my back rank, checking my king, and immediately rasied his hand and announced "checkmate!" The teacher came over, looked at the position on the board and asked me something like "Are you sure this is checkmate?" (I don't remember the exact words, but it was a lot less obvious.) I had lost all of my previous games, so I was sure that it was a legitimate checkmate, and I said yes. So I said yes, and the game ended with me resigning. Then my teacher showed us that I could have blocked the rook with my bishop (which would have been protected by my king). My opponent just said "yeah" in a very nonchalant way, as if nothing had happened.