Episode Seven, “Equally Dead Inside,” has Jimmy and Gretchen acknowledging that they won’t sleep with other people, but they still don’t think much of whatever it is they have. In fact, Edgar is more ecstatic about this bond than either Jimmy or Gretchen. They aren’t, as Edgar puts it, boyfriend and girlfriend.
They’ve just made a verbal agreement to not sleep with other people. So close enough, but with more words and less lovey-dovey stuff.