Sorry soccerdad, I personally view it as emotional infidelity. She, the OP in midst of excusing behavior that to her damages the relationship. This isn't judging his past behavior, it's in the here and now. She states she's been open and upfront about her discomfort.
Her T raises a very valid point and her bf is man enough to end it...very commendable.

It will take some work on OP's part to move past, won't be overnight. Involves a sense of betrayal. But, again, her bf said he'll stop communication, perhaps, something nagged at him, a sense of discomfort?