~~If the bet is successful, Polymarket pays out — just like how more conventional betting works ~~ (Edit: this is incorrect — it uses matched betting. See the comment below mine for more detail)

In terms of who determines which way a bet goes, it seems like this is also Polymarket, and that they rely on journalistic coverage and official announcements.

This journalist reported that one of the missiles landed and exploded, and it appears that this was used to deny paying out to the people who places at bet that no missiles would land that day. The gamblers tried to coerce the journalist to change their report to say that all of the missiles were intercepted, and that the thing that actually landed and exploded was just a missile fragment from the intercepted missile. I have no idea whether this would've actually changed the outcome of the bet from Polymarket's perspective, but the gamblers certainly seemed to think so.

It highlights the absurdity of betting on events like this

What's even more fucked up is that there's nothing preventing DoD employees from also betting on this stuff while simultaneously being the ones deciding the who, what, when, where, and why of bombing another country.

Shayne Coplan is the billionaire manchild who owns polymarket along with a couple other billionaire cofounders like Peter Thiel. It's just like bookies with details decided before the bet is made, and the house/market/organized crime organization take a cut for guaranteeing the bet pays out.