The guy you were fighting was more or less one handed, just winging that right hand. You fed into that by doing three things. First, staying right in front of him. Second, pawing with your jab. Third, putting your hands up and waiting on the punch. If all he's got is that right hand, circle to your right, make him punch across his body. A lot of times his right hand was real wide, while other times he telegraphed it by picking his right elbow up and 'aiming' the punch. these are things- making him punch across himself and picking up on when he's going to punch- that enable you to land counters.
You, also, telegraph the right hand by picking up the elbow before you throw it and you are real slow at getting your punches off. Just shoot them. There were times when it seemed like your opponent was winded and didn't want to fight, was maybe trying to catch his breath. In those instances, first you weren't able to walk him down behind a jab. Second, when you did get close and start throwing punches, you'd square up and drop your hands and he'd sting you, once with a left. Generally, he'd wing the right and you'd back off.
Get sharper with your punches and work on your defense. No reason to be eating right hands like that.