Nah, definitely not the main reason. I think Beth is more just a side character you sleep with, plus it's not swinging. Sharing, yeah, but not swinging. It's more the Lilith/Abby relationship, since Lilith and Abby are both love interests, and the MC is sharing his love interest with someone else.
She could be but for now, she did nothing in that direction
This is mostly at tbarton, but your argument doesn't really fit what's happening. Beth and Vanessa have been pretty integral in the story so far, and as of the most recent updates
they may even become part of the family.
But really, you have two couples -- Lilly/Abby and Beth/Vanessa -- and Frank is sleeping with one of each. But only one of those couples is married. I've never heard the term "swinger" used outside of married couples before (which doesn't actually mean much), and since there's only one involved with the MC at the moment, that seems more likely to be the reason for the tag ... at least to me.
EDIT: You're right, it's not "technically" swinging (by my understanding of the definition), but nothing else in the game so far even comes close to the definition, so that's why I think Beth is the main reason the tag is there. I'm not arguing whether the tag is correct, just why someone may have put it in. The tag is not in the OP description, just the one generated for the page.
EDIT 2:
[Swinging] by this site's definition "A couple allowing one or both partners to have sex with a third party."
...
"Sharing" does not exist as a tag.
This means Beth is the ONLY way the tag could be in place, since Abby doesn't know what's happening; therefore she can't be "allowing" Lilly to sleep with Frank, and no-one else he's been with is established to currently be in a relationship with anyone (other than Frank, that is).
[Edited to reflect that I have now read the site Tag definitions, including "Swinging"]