Off campus the “cop” has no jurisdiction. Unless the dead guy threatened the “cop” with deadly force, this is murder.
I vote for murder.
Not necessarily. I don't know how it is in Texas, but in California, a cop is a cop. A cop from SF on vacation at Disneyland can legally arrest someone committing a crime. While there may be some political issues with a cop stopping someone while outside of his "jurisdiction", as long as it is in state, there is no LEGAL prohibition from doing so.
Of course, he has to be a sworn police officer, not a security guard or rent-a-cop...