If the CSI franchise was deeper and explored the characters more, I think an argument could be made that Jamie was playing a sociopath. Usually the killers on these type of shows have some sort of emotional reaction to being caught, whether it's anger, fear or remorse. He just smirked. And he could have just knocked the girl out and fled the scene, but he continued to beat her with zero emotional response.
I watched the original CSI for several seasons, but never could get into the spinoffs. Both the Miami and NYC versions were on the bubble for renewal this past season.