Yes, he was on the run (again) after he killed this gal. Why he killed her was the mystery, and so she was messing with his laptop. Not really a thing to kill over unless there was something on it he could not let her know.
Of course I can only guess why he would confess, there is no doubt he and she went to his room and only he is seen leaving in different clothes and his luggage. Leaving instructions for the staff to not bother his girl.
“...so she was messing with his laptop. Not really a thing to kill over...”
Obviously, you don’t know anyone well, or haven’t lived with someone, who has no impulse control. The tiniest thing (or non-thing) will set them off. It doesn’t have to make sense and it doesn’t have to be a big deal. A lot of wives spend their lives walking on eggshells simply to avoid being physically abused, or dead, wives. You add booze into the mix and it’s worse. Considering where Joran picked up the girl, there’s a pretty good chance they were drunk.