As others have noted, same-room stuff with other couples comes later in the game. But to the extent that Anne openly has sex with others, the MC semi-openly has sex with others, and in one case they're both involved, I'd call that swinging.
I mean, this has been discussed for 200 pages now. The game was originally called The Cuckold, and as far as I know your save files are still in a directory entitled that. The MC's fetish is for Anne to fuck other guys, and he repeatedly makes that explicit; the only reason there's all the more limited exposure and teasing at the beginning is that he's trying to work her up to it. The MC's other fetishes are to watch and/or hear about it. Actively participating with her isn't that important to him, and fucking other women is something he does without seeming to care how Anne feels about it. If that's not painfully obvious from the dialogue, think about the challenge game that gets the story going. Are any of those challenges aimed at the MC, or them as a couple? No. Every single one is about Anne doing something more outrageous than the last time.
Playing the game as if it's about either the MC or the player controlling or limiting Anne's sexuality is completely missing the point, and anyone who tries to play it that way is never going to be anything but frustrated. The game's not about trying to stop Anne from having sex with other people, it's about how to manage their (mostly her) extracurricular activities in the context of their relationship. Will it be open? Will he respect her autonomy? Will he respect how she feels about constantly being pushed to have sex with other people? Will he be honest about his own dalliances? Will he continue to devote himself to their relationship, or will the fact that she's getting laid and he's getting laid but they're no longer intimate as a couple lead her to decide that he really doesn't care about their marriage anymore?
The reason there's not more swinging content is largely because it requires entirely separate scenes and renders. Anne can have sex with X and it can be in the context of an open relationship or not, it can be something the MC sees while it's happening or hears about afterwards (or that we as a player see while the MC's elsewhere), it can be with the MC's support or it can be Anne cheating. But whatever it is, aside from some minor dialogue tweaks it's the exact same scene. Doing an entirely separate set of renders so the MC can choose whether or not to join in slows everything down. Also, as I said before, it's not the soul of the game. For instance, the scene with Mike...the scene where she's alone with him is vastly more intricate and hotter than the threesome. I think that's deliberate. Later, if you're on the Dre path, Anne will make it clear that she wished you hadn't joined. I too would like a balanced swinging game, but this isn't it; this is a game where they'll both have sex with other people, but the story exists to explore the MC's fetish for Anne to sleep around and the consequences that has for their relationship.
Well, if you insist on playing it that way you're fighting the game. I'm not telling you that you can't or that you can't wish for a different sort of game, but you're in for a lot of disappointment.
The MC has two potential encounters in Punta Cana, though I don't recall if you can get both of them in a single playthrough. One has very serious consequences for the future of their marriage, depending on what Anne's done and how you've reacted to it. For example, if you come into it playing the game the way you have, you'll...regret it.
This has probably been answered fifty times over the last however many pages. A lot more scenes. Better renders. Better game logic.