After the race, the horse owner and the bettors get a payout of their winnings. The payout system is fully auto-calculated, therefore there is no place for manipulation. It is based on preset algorithms, guaranteeing there is no room for miscalculations.
The bettors can play without actually being online. There is no need to administrate the races, they can be run completely automatically. The owners of the horses can register their horses for future races, which can also happen with them being offline.