No he didn't. He had just defended himself against two assailants, while trying to flee. He was never, at any point in time, an "active shooter".
An "active shooter" is "an individual actively engaged in killing or attempting to kill people in a confined and populated area; in most cases, active shooters use firearms and there is no pattern or method to their selection of victims."[0]
He had a pattern of selection. Kyle shot and neutralized those who were trying to kill him (or cause grievious bodily harm). That is, by definition, self-defense, not an "active shooter" event.
[0] https://www.dhs.gov/xlibrary/assets/active_shooter_booklet.p...
QED.