Apparently the decision to delay the movie had more to do with the shootings, even if the issue of the country being awash with guns and shootings is not something you solve with moving B movies around the calendar. But I assume it made enough sense to the studio at the time, at least compared to the media circus about Joker.
It would have been really dumb to make the decision just off Trump's comments, since the delay pushed the movie right in front of the start of the pandemic theater closures, and at that point Trump was probably too busy mishandling the pandemic response to care about The Hunt anymore. And if he really brought up videogames? Even dumber, conservatives have been scapegoating videogames for decades. And they cycle through outrages and culture wars all the time. They took on Barbie last, which is now the biggest movie of the year and will remain that way.