Why is this not checkmate?

Qg2 and there is nothing to prevent the K from capturing.  Qf2 is backed up by the knight, so it's mate.

Thank you very much! I understand it now!

We were all beginners once...

A year ago I was around 600 rated thinking: I'm so good at chess! I could beat my whole family besides my dad.

Then I went to chess.com, and I was disappointed that I was not even average.

Many years ago when I was our high school chess coach, I met a young man in class who bragged to me over and over how good he was and that he could beat  his whole family with no problem. I finally sat down to play  him one day, and crushed him unmercifully (note, I'm only about a 1250 player, nothing to boast of). Needless to say, he realized quickly that there's more to the world of chess than Uncle Larry.

Reminds me a bit of the time a high school junior rated 1600+ was holding down the chess club table at the activities night for next year's incoming freshmen.  As one father and son walked up he casually said "there's nobody in the building that can beat me!"  The father asked to set the board up and the kid found out after losing that he had the bad luck to say that just as the 2000+ rated father was stopping by. The 1200-strength teacher that was the team's faculty-member coach had recognized the father straight off and sat back quietly figuring the kid could learn a lesson about discretion.

High school coaches are used to getting e-mails about a kid unknown to them being great and their team's new first board.  With the rare exception of an unfamiliar but strong player moving in, the claims are invariably wrong.

The white king can capture the black queen on g2.  That's why that's not checkmate.