I think part of it is cargo-culting and/or esthetics, and the seduction is a bit more subtle, their betting markets formalizes their belief:
That if people believe something (they agree with, they aren't consistent with it), that thing is more likely.

Some might even have an actually "occult" interpretation and see it as a form of actual divination. Yud certainly appears to me to have that tendency.

Because there was an influential person decades ago who framed subjective probability and rationality in the face of uncertainty in terms of betting. Therefore it is gospel among Rationalists. Meanwhile, their non-zero probability and infinite negative payoff in the face of the acausal robot god leaves them trembling.

I think the simplest explanation is that it appeals to their urge to ruthlessly quantify all human interactions, including statements about their worldview.

I think it started with Robin Hanson, one of his Big Ideas is that public policy should be decided by prediction markets instead of democratic processes. He calls this hypothetical system "futarchy" and lesswrong is one of the very few places it's taken seriously.

In the bigger picture, I think it's popular in Rationalist circles because it just fits in with their biases. Using markets to evaluate truth claims gives a plausible-sounding excuse to disregard expert opinion, and (much like their "Bayesianism") gives their personal opinions a veneer of precision and objectivity via quantification.

It's perhaps worth noting that FTX also ran prediction markets before it collapsed.

Reading this reminded me of a certain OG wager -

https://en.wikipedia.org/wiki/Simon–Ehrlich_wager

In theory, a prediction market can work. The idea is that even though there are a lot of uninformed people making bets, their bad predictions tend to cancel each other out, while the subgroup of experts within that crowd will converge on a good prediction. The problem is that prediction markets only work when they're ideal. As soon as the bettor pool becomes skewed by a biased subpopulation, they stop working. And that's exactly what happens with the rationalist crowd. The main benefit rationalists obtain from prediction markets and wagers is an unfounded confidence that their ideaas have merit. Prediction markets also have a long history in libertarian circles, which probably also helps explain why rationalists are so keen on them.