Why did he quit the football team? [spoilers]

Yes "he" was the one who's Mom left and yes "he" was the one who tried to overdose toward the end of the film. As for the reason for quitting the american football team, "he" did so because "he" didn't want to play american football. "He" quit because "he" didn't want Kent (dad) to live his life vicariously through him.
All of which were made perfectly clear to anyone paying proper attention to the film.
As was his name: Tim.

I think his fixation on the online game played into it since it was mentioned more than once the amount of time he put into it. His mom leaving affected him quite a bit, and it was probably partially a cry for help.

Wasn't he going through an existential crisis? He repeatedly refers to the Carl Sagan "Pale Blue Dot" concept that in the grand scheme of the universe, nothing we do really matters. With this in mind, and in light of his struggles with possible feelings of abandonment from his mother leaving, he felt that playing football wasn't worth it. Of all the characters, he probably had the most fully-realized story arcs (he and Brandy could even be called the "heart" of the movie), because throughout the movie, he feels that his life is insignificant and that if he were to disappear, no one would notice, but in the end, when he tried to kill himself, his father was heartbroken and his girlfriend was by his side. It was not at all surprising that he would try to kill himself given the situation, though: he believes his life doesn't matter, and watched his mom leave him and shut him out of her life; the game was a community for him to feel connected with online friends, and his dad severed his ties with these people; his girlfriend, as written by her mom, not only rejected him, but in a heartless and aggressive way, immediately after he told her that he was feeling alone. Really, though, it comes down to the Carl Sagan influenced crisis he was experiencing.

He was staying alive to play guild wars 2. People do this when they are depressed and feel like they have nothing left in their life. When you play an MMORPG people start to depend on you, and miss you when you're not there. You feel responsible for something. Then he met a girl he liked, which gave him another reason to live. Somebody who actually gave a *beep* about him. Somebody who made him feel wanted, and needed, and was probably in the process of replacing the need to play GW2. He felt like these two things were 100% of the reasons he had to keep going, because he was needed.

His dad deleted the game and cut off his subscription to the game (we're supposed to forget guild wars 2 isn't pay2play) and the girls mother made him think the girl never liked him and never wanted anything more to do with him. Both of his reasons to live were gone in the space of a few minutes.

(he wasn't depressed enough to kill himself at the start because he had GW2)

"There are always rewards for those who state the obvious frequently and with conviction."