I doubt she was on his computer. He probably has it password protected. This albi might have held up if she had her clothes on.
I don't think he planned on killing her when he brought her up to his room. It doesn't make sense. One's own hotel room is one of the worst possible places to commit murder. A deserted beach late at night (such as they have in both Lima and Aruba) is much better. I think he flew into a psychotic rage and simply couldn't keep himself from killing her.
IOW, his story of how it happened is probably true. He goes out to get coffee and bread. She opens his computer to check her email or Facebook account, then googles him out of boredom. Uh oh! About then, he returns, she confronts him, and he explodes and kills her. Then, realizing the mess he's in, he pays for two weeks' additional stay, instructs the hotel staff to stay out of his room, and flees.
This albi might have held up if she had her clothes on.
According to reports, she was not sexually assaulted.
One additional mystery is why she went to his room in the first place, given she was gay.