Is it possible that Chet called in it (or his manager) just to possibly use it against him? They didn't know that "the pawn" would occur and used it to their advantage later. BUT, it could be a way to control him if he got out of line (according to their perspective).
By the way, 9/10 (BRILLIANT!)
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The watch is the probably the hardest plot element to figure, in my opinion. I believe the best explanation is that these guys planned everything to get Mike to fight, and they didn't pay Joey with the intention that Mike would give him the watch specifically because of this. When it turned out to be hot and Joey couldn't get money for it, they figured this--and the scam his wife was pulling about the Brazilian fabric--would be the reasons Mike would fight on the undercard to get cash.
I'd love it if Mamet just told us what the hell he was thinking. But my interpretation is:
Mike meets Chet in the bar and saves him by accident. They legitimately want to use him as an 'advisor' (given how unscrupulously they act I don't think they plan to actually credit him) but, as Joe Mantegna says, the watch surprised them. When the watch was discovered to be 'hot' they just distanced themselves (canceling the numbers, walking out of the restaurant) because of potential embarrassment from the stolen property, plus the story coming out of Mike rescuing Chet.
But before that happened, Mike had hinted at the stone game (at the dinner meeting). The wife, desperate for cash and being a bitch whore, went to her brother and offered to give him and Chet the details of the 'gimmick' in return for her clothing deal, waiving her debt, and probably some of the resulting cash. To stop Mike from suing she gave them the spent cartridge.