Tragedy
How do we know Timon of Athens is a tragedy? Well, our first big clue is that the title character falls from grace and dies by the end of the play. This could be because of his own fatal flaws of overindulgence or excessive spending, or it could be because of Timon's ruthless cohort—or both. Either way, the dude winds up miserable and very, very dead.
But this play isn't a totally normal tragedy: for one thing, it's the only Shakespearean tragedy where the main character dies off stage (and under mysterious circumstances, at that). We're never really given insight into the circumstances surrounding his death; Timon announces he's working on his epitaph, and then abracadabra, next we hear, he's buried.
It's clear that the play's main interest isn't in fulfilling the all the typical requirements for a tragedy. So what's this play all about, then? Well, some scholars think this is kind of an experimental play for Shakespeare. It's basically a tragedy, but it's got a lot of elements of social commentary and urban satire.
Timon himself is part of that commentary and satire—he's not a totally sympathetic character, after all, and the play is less about him than it is about some bigger issues like the nature of money, power, and justice.