In English this could mean he is going to stop taking bets on something. Does it have this meaning in French?
No, there is no figurative meaning in French.
Is this a betting reference?
Could this be metaphorical? The English version could be understand as 'he's going to take no further action (on a matter).
No, the metaphorical expression is "il va clore le chapitre" (lit. close the chapter)