First off, Greer was not trying to apprehend Miller.
Greer intended to kill Miller.
So even if Greer had been a cop, this still would have been murder because he made no attempt to capture Miller.
But, as to TN v Garner...
The case seems to say that Greer's shooting Miller would not be a "good shoot".
TN v Garner itself deals with a burglary suspect who was shot by police while fleeing. That shooting was ruled a bad shooting.
TENNESSEE v. GARNER, 471 U.S. 1 (1985)
"While burglary is a serious crime, the officer in this case could not reasonably have believed that the suspect - young, slight, and unarmed - posed any threat. Nor does the fact that an unarmed suspect has broken into a dwelling at night automatically mean he is dangerous."
"Where the suspect poses no immediate threat to the officer and no threat to others, the harm resulting from failing to apprehend him does not justify the use of deadly force to do so."
"if not now later" doesn't seem to meet the bar of "immediate".
but perhaps the mileage varies for some