Does it seem that most gay men in open relationships
1. play together only
2. play without their partners but talk about the experience with their partners, or
3. have a don't ask, don't tell arrangement?
I know different couples who do either 1 or 3, and also those who do a little of each. I don't believe any of our friends play separate but share about it afterwards. Some examples:
I know a legally married gay couple that practices leather bondage. They have an "equipment room" in their house (I hesitate to term it a dungeon), where they participate in scenes that sometimes include others (not me, BTW).
Another married couple will sometimes bring a new acquaintance home with them they met in a club, for a 3-way. They're another pair I've never done anything with myself, although there were a few times I was pretty sure one of them was testing the waters with me. But I was already with my current guy, not single and not available.
Maybe if I was single again. Because I did have 3-ways, even 4-ways with other couples in the past, when I wasn't in a relationship. So I have indisputable knowledge of gay couples who play with others together. A number seem to already have a rocky relationship, perhaps the sexual games meant to spice things up and keep them together.
But they still eventually split. Except for our friends I've mentioned, who have been together, and behaving this way, literally for decades. They seem to know how to manage it, to strike the right balance, with very clear mutual rules they never violate. I can't answer your "why" question except maybe to chalk it up to male horniness, that some guys can isolate from their stable relationships without damaging them, while others cannot.
I also know couples who permit each other to do individual stuff on the side. But it is indeed "don't ask, don't tell", and of course don't get involved and don't bring anything contagious home. I've likewise known that practice to only be successful for a while, yet with at least 1 long-running exception.