Many people believe that you have to have sex to commit adultery. This is not true. As you have highlighted, being unfaithful to your partner has many disguises, and this includes forming an emotional attachment to someone else.
Even though you broke up with him, this is one occasion when you can and should implement no contact. Your gut is telling you that he wants this other girl, and he hasn't shown any interest in getting back together with you.
It's time to let him go and move on with your life.