Obviously there is more to this shooting than the cited story details. But I fail to see a self-defense angle in it.
Maybe he had eyes in the back of his head
And yes I can see that as self defense in certain cases.
Someone tells me that are going to kill me I do not have the luxury of assuming that they are a liar.
However in this case, lacking any sort of background, I would say that this does not appear to be self defense.