Somebody explain the rules please

how can this game be drawn after the timer ran out

It says there - game drawn due to insufficient material. You cannot check mate with a knt and king. 

Since your opponent ran out of time, under normal circumstances he/she should have lost. But since you did not have enough material to checkmate your opponent it was a draw.

That makes sense. But this rule sounds stupid in a timed game. During the game when we both were around 3 minutes, I had only a knight but the opponent had a knight and a bishop. I worked hard to beat those two pieces and at the end this guy walks off with a draw. Whats the point if me taking away his pieces after hard work just for a draw. While he sits back and does nothing because of this stupid rule.

I think it's even harder to lose on time if the game is not timed.

And your opponent didn't just sit back and did nothing. He took all of your pieces (except the knight), too!

It does seem stupid but it would also be stupid to carry on for several minutes or more ,when no one can win just to see who runs out of time, there would be no chess just moving as quick as possible.

Black must have run out of time. White has insufficient material.

Under FIDE rules that would have been a win for white. It is possible, though unforceable,  for white to checkmate black with the material on the board. I believe under USCF it would also be win for white since black still has a pawn.

ECF if this goes to adjudication would agree martin

I thought under USCF rules white would have to be able to force a win ?

I'll have to grab the book to be certain, I know some of the rules read that way. I may actually be thinking of two knights for the stronger side and the weaker side has the pawn in cases of a flag fall.

it is a flank pawn too which are very tough to promote

Yeah, you are right. USCF it would be a draw, unless there was a forced mate on the board. I was thinking of the case of two knights, which specifically calls out the opponent not having a pawn for insufficient material on flag fall (along with no forced win).

In the final position there is a series of possible legal moves that would lead to checkmate - final position with white, Kf1 and Nf2, black with Kh1, pawn (but not a promoted bishop) on h2. 

 Chess.com has combined two rules, "Insufficient material," and "Insufficient losing chances" (USCF terminology, FIDE has equivalent rules) into one,

 "Insufficient losing chances"* applies before the flag falls, and requires that the clock be stopped and the TD asked to adjudicate the game a draw.  Since there is no way to have a Chess.com game adjudicated, the staff incorporated the concept into "Insufficient material."

* An example would be K+R vs K+R

Do you guys think that this game would have also ended in a draw? I had less time here than my opponent, but the opponent agreed to draw it out instead of letting me "lose on time". 

I think that's a draw.

I understand it. But too hard for my princess head to get with it. Like for example, I have only a knight and a king in the middle of the game and opponent has 3 or 4 other powerful pieces. While, he knows he can win, considering the presence of his pieces and the fact that I can't get anything more than a draw, I, on the other had, have to motivate myself to play for a draw, where also a loss is possible for me. The opponent here is with a clear psychological advantage than I am. While the opponent can either win or draw, I can only draw or lose. Chess is a logical game, maybe too much logical for humans. I think chess should be played only between computers or Artificial Intelligence, since they need no motivation to win, draw or lose a game.  Or may be timer should be shut-off in such a position, where one player has only a knight and a King. Because What is the point of me using my head quicker and still ending up with a draw. They might as well shut-off the time. It is annoying to know that I used my head more effective than my opponent and still end up with a draw.

Wait a minute, the game itself is unnecessary. That is what makes it worthy IMHO.

Assuming that this is a chess.com game (Post 19) and you ran out of time, I think that you would lose.  The chess.com criteria for insufficient material are fairly simple, and this position would not meet them.

The criteria were developed several years ago, and I don't remember them, but they are similar to the USCF criteria.