You probably are aware of this, but Pi-hole itself does not block anything. What gets blocked is determined by what block lists, and blocking entries you have added.
As I see it, you have to continue trying by looking at the query log to determine blocking activity around the time you launch the game, or try to make an in game purchase. Then add the domain to the allow list.
I guess you could try disabling blocking for a specific client. See https://discourse.pi-hole.net/t/disable-pihole-for-a-single-client/53582