No, at worst he is guilty of 2nd-degree murder, which is not a death-penalty offense.
Tensing should get a medal, a commendation, and a huge bonus for taking out the trash as he risked his life on the streets.
See post 33.
Either those clips from the actual video have been shopped and doctored, or Tensing really in fact was under assault, was dragged for several seconds, but was able to get a shot off before he was knocked to the ground.