Is papa-katsu (compensated dating in Japan) cheating?

When I was invited out to dinner by a woman I've been seeing for over three years—not through a club or app—she told me, “My boyfriend asked me out to dinner today, but I turned him down!” I said, “Wait, you traveled with me last week, so you haven't seen ○○ (your boyfriend) since then either. Is that okay?” She replied, “He hasn't found out, but he's kind of annoying, so it's a hassle. I do feel a little bad because I guess I'm cheating on him with you, ○○, but I have more fun with you.” That got me thinking: What does “cheating” even mean in this situation? We seem to be very compatible, so we meet three or four times a week for dinner, overnight stays, and dates. I only receive an allowance when we have an adult relationship (intimate); I don't accept anything for dinner or regular dates. So, from my perspective, we're in a transactional relationship, and the word “cheating” doesn't really feel right. It's basically no different from going to a soapland, agreeing to a private arrangement, giving her some spending money, and going all the way—so does papa-katsu count as cheating? You could also consider visiting an adult entertainment establishment cheating, but somehow the word still didn't feel quite right to me. Is papa-katsu cheating?