I have an ex who did the same thing to me.

I didn't realize he and I were even in a relationship (last I checked both people must acknowledge and agree to it for it to be a relationship.) AND he told me I was free to sleep with who ever I wanted. Until I actually did, then it became cheating. (He then proceeded to use it against me at every available opportunity. Should add this one turned out to be emotionally abusive.)

If you didn't feel there was a relationship then I don't see how it could have been a relationship. So, no, I don't think you cheated.

I do not think there is much point trying to hold on to this relationship though. It seems quite unhealthy and if you need to tell him how much better someone else was, probably not a good fit for either of you.