From here it appears he's lying if he claims to not be dating her and yet he acquiesces to her demands about his relationships. No healthy, functional adult would worry about the demands of somebody with whom there is no relationship--which indicates there is.
Or it indicates that he's got major problems and doesn't qualify as a healthy, functional adult. If he's put up with as much co-dependent shit from her as it appears, I'd say he's likely not a healthy, functional adult.
I'd stay away from that mess completely, were it me. No dates, certainly, and no involved chats or visits or anything else. Nothing until I was firmly convinced his Bucket o' Crazy is much smaller than it appears right now.
When speaking of various forms of non-monogamy...it ain't poly if you're just fucking around.
While polyamory, open relationships, and swinging are all distinctly different approaches to non-monogamy, they are not mutually exlusive. Folks can, and some do, engage in more than one of them at a time--and it's all good.