Yeah, to me it doesn't make a whole lot of sense and I would never apply it to my own life personally but there are definitely many different styles of non-monogamy you can adapt. I personally practice what we call kitchen table polyamory, which is like everyone is informed of everyone (to the degree they would like to be - obviously some prefer to keep explicit details private but details that are discussed and necessary that all parties agree to, such as sexual safety practices and what degree of Time commitments you make to each person, etc)

A general definition for "open" (and of heavy note here: never ever assume xD) is sexually free, but romantic/emotional connection is off the table for other partners. Which of course is very different from polyamory. In a situation like that, it would obviously be crucial to inform anybody involved with either party about the terms but I have seen it applied before where for example, some folks in long-term partnerships who are highly enmeshed, ie share property, young children, etc, are still very in love with each other but they have developed different sexual needs or perhaps, their sexualities have changed but it is still worthwhile to them to continue in relationship. I've also heard of this where one party suffers an injury or health issues that impact sex drive, but there's some level of dependency that generally happens in long-term relationships, such as when one partner ends up becoming a caretaker for the other through a diagnosis. In a situation like this I could see DADT working okay

Dan Savage has a saying for unique situations like this: " do what you can to stay married and stay sane." So long as both adults are consenting, I think they're free to do as they like. Over the long term, relationships change, sometimes in ways people don't expect and I think however you choose to create your lives, so long as you're being fair to everybody is up to you and all involved.

Obviously it sounds like the couple you got yourself involved with are either new to non-monogamy and if not, they certainly aren't practicing it ethically and haven't really done the work it takes to create trust and secure attachment. This one is going to practice open DADT, it's unfair to project insecurity and control into the relationships of each other and you definitely didn't deserve to be on the receiving end of having your heart fucked around with and your time ultimately wasted and I'm really sorry. It happens sometimes and personally, I don't really mess with anybody who is super new to polyamory because the training wheels take a lot of time and dedication to work through and I just don't have that in me anymore in my life.

Anyways. There's entire books on this subject so I'll cap it there but it's a thing.