Moss is like the angry brother who feels his sibling always gets all of the attention. Moss is #2 on the contest board, which means he will at least get to keep his job, but that's not what he wants. He's tired of the way things are run, and it's safe to say he's tired of being second place to Roma.
Moss's main function in the play is to get the ball rolling on the break in—he might not be able to go toe-to-toe with Roma, but he can surely have his way with Aaronow (and Levene, it turns out). While Moss and Aaronow eat at the Chinese restaurant, Moss engages in some semantic acrobatics and basically convinces Aaronow that even if he doesn't rob the office he's going to go down for the crime anyway:
AARONOW: You want me to break into the office tonight and steal the leads?
MOSS: Yes. (Pause.)
MOSS: Oh, yes, George. (1.2.321-326)
While we see Roma actually make a sale, this is Mamet's way of showing us how Moss might approach the job. He manipulates and leads his prey down a path, lying without a thought (he tells Aaronow on multiple occasions that this all just hypothetical), and then pouncing.
We find out later that he doesn't close the deal with Aaronow, but we also find out that he did close the deal with Levene. Both Aaronow and Levene are off the board. They're the ones who are going to get fired when the contest is over, and Moss isn't stupid—he knows what desperate men will do.
Moss lacks the panache of Roma, the sympathetic nature of Aaronow, and the journey of Levene, but that doesn't mean it's not a great role for an actor. His scene with Aaronow is an exercise in subtle shifts, and not just anyone can pull it off:
AARONOW: Yes. I mean are you actually talking about this¸ or are we just…
MOSS: No, we're just…
AARONOW: We're just "talking" about it.
MOSS: We're just speaking about it. (Pause.) As an idea. (1.2.238-243)
A couple of minutes later, Moss drops some science on Aaronow, and we know that he's been actually talking about robbing the office the whole time. For an actor playing Moss, the trick is deciding how good he is at covering up his true intentions. He's obviously pretty good at it, because he lures people in and gets them to do what he wants… and then he heads out of town professing his anger and innocence.
It's easy to look at Moss as the Beta dog to Roma's Alpha, but there is more to him than that. He has his own desperation and he's reached the tipping point. Even if he is just a Beta dog, watching him try to find situations where he's #1 is one of the most interesting parts of the play.