Does this refer to "at any point prior to July 31, 2023", or "check the site on July 31, 2023"?

Republicans are currently favored and were when the market opened, so clearly the latter. @SamLichtenstein 

@SalemCenter Then how about changing the title from "by" to "on"?

This market will settle YES if by the end of the night on July 31, 2023, Republicans are favored to win the presidency in 2024 according to the website Election Betting Odds. 

https://electionbettingodds.com/PresidentialParty2024.html

In the case of a tie, the market will resolve to YES. If Election Betting Odds has no estimate, then the market will settle according to who is the favorite on Betfair. In case no estimate is available on Betfair, the market will close according to the odds on another prediction or betting website to be chosen later. 

To be clear, "by the end of the night" means at that moment, not Republicans being favored at any point in time between now and the close of the market. 

Play-money betting