When I look at the known facts of the crime and the possible motivations that fit those facts such as misogyny, revenge (probably for a narcissistic injury), or enjoyment, all of the motives point to a narcissist/sociopath/psychopath.
Also, someone already posted a tweet from someone in MSM that included a portion of this quote:
"Roberts started the program in August — along with Kohberger, he said — and had several courses with him. He described Kohberger as wanting to appear academic.
'One thing he would always do, almost without fail, was find the most complicated way to explain something,' he said. 'He had to make sure you knew that he knew it.'"
Source:
What We Know About Bryan Kohberger, Suspect in University of Idaho Murders
As averred by the other poster—sorry, I don't recall who it was—that is classic narcissistic behavior.