"Obsessed," like other words we've seen used in this case (when the BK relative tossed out "OCD" when he has not been diagnosed, so far as we know) has meaning both in ordinary discourse as well as in professional contexts. I'm not a psychologist but I can say that some people are "obsessed" with K-Pop or TikTok or NFL football without meeting any sort of diagnostic criteria.
It's possible, I think, for a fairly cold-blooded person to wonder what mass murder is like, decide to find out, and then carry out the crime. I don't think, for example, the Pennsylvania spree killer Stanley Hoss (1960s-70s) had obsessive thoughts. He was an opportunist. He had a chance to escape jail, so he did. He had a chance to rape a woman, so he did. He had a chance to shoot and kill a police officer, which would allow more escape, so he did. He had a chance to kidnap and kill a woman and her child when he stole her car, so he did. In prison, after he was caught, he had a chance to kill a corrections officer, so he and other inmates did. With no more thought than an eagle catching a fish for dinner.