Weather derivatives are a thing, traded on CME. They have a centralized clearing function. It works nicely.
Prediction markets exist in many places with centralized exchanges/clearing houses. If there is enough volume, the market works, if there is not, it doesn't. They exist for most financial securities, commodities, sports, various weather events and probably many other things I'm unaware of.
They mostly use a central party and (i'll guess) a pretty standard sql database. Before the financial crises some of the trades were done bank to bank with (horror...) no intermediary.... like people just called each other and kept distributed records and settled up...