> I honestly don't see the problem with someone gaming at 2pm

It depends on if other team members need to be able to reach out to this person at 2pm

Even when I was working in an office I would sometimes take 2 to 3hours bicycle rides at lunch time because it was the best moment to be doing sport outdoors in winter.

I would just make sure I had no scheduled meeting and had people in my team available. Sometimes I would do it to make up for extra time outside of office hours. This also allowed some of my coworkers to leave earlier because they knew I would stay longer to do my regular shift.

What if a team member needs you at 12am?

If there's a need for "core business hours" those can be established. My most recent company was evenly distributed around the globe so needing someone at 2pm PST is not much different than needing someone at 12am PST.

The vast majority of companies I've worked at remote have a strong async culture and are better for it. With some obvious exceptions, if you need a response in 15 minutes there's something wrong with your planning.