yes sir, it's checkmate !!!!
Is this really checkmate?

Yes. The immediate threat has to be dealt with first. That's the beauty of that rule, if you use it to your advantage. Sometimes you can distract or move an enemy King away from another piece if that piece is already pinned.
3...Kd8? (...Kc8 would delay mate two moves I think) 4.Qa8#!
Ha, yes, I saw that. Thanks for pointing it out.
Just out of curiosity, what if it is white's move and the black King is on h1 instead of the apparent a8?

The computer said it is checkmate too. And it always wins when we play chess. However, I always win against the computer when we kickbox.

The original poster know that it is checkmate but is asking a logical question. Yes, it is checkmate. But he asks why? Because, under the rules of chess, the king is in check and CAN NOT MOVE INTO A CHECK. Therefore checkmate and the GAME IS OVER. The OP is extending his logic past the point of where the rules of chess dictate the game is over.
Interesting side note; I have noticed that when you move a piece, but BEFORE you hit submit, if it IS checkmate, the little box that lists the moves gives you the checkmate symbol. Now this is unlikely to help anyone but the beginners but you could, theoretically, test out several moves before hitting submit and stumble across a checkmate you didn't see. That doesn't seem fair to the beginner on the other end of that mate. It shouldn't tell you it's mate until AFTER you hit submit.
im a beginner, and, i find it useful, because sometimes i think something's checkmate and it isn't (as in the horrible game a played a few weeks ago where my queen was taken)

im a beginner, and, i find it useful, because sometimes i think something's checkmate and it isn't (as in the horrible game a played a few weeks ago where my queen was taken)
That's exactly my point. You really need to learn those things to get better. You won't get that kind of help OTB (or on other chess sites) and it's not really fair to your opponent.
If you get stabbed on the throat does it matter that you had a knife to your enemy's kneck?