As OP said they were on and off for about 2 weeks at a time.  If they had been separated for a longer period of time like 4 -5 months it would be different but he and she both likely knew they would be seeing each other again so yeah it was cheating.  Any couple in that situation who knows there is a chance they will get back together would know that to have sex with someone else is wrong. 

True that he invaded her privacy but most people would rather know the truth than not know.  She clearly was not being honest with him.