No, what makes it an officer involved shooting is it involving an officer. They don't call the Texas Rangers for every shooting that happens in Dallas. Nor do we discuss it.
My understanding is that the Texas Rangers were called in because it is not appropriate for a law enforcement agency to investigate itself on any potential criminal act of any officers. The Dallas police chief indicated that in order to maintain transparency they invited the Texas Rangers to conduct the investigation on their behalf and she made a point of indicating that it had nothing to do with lack of confidence in her officers/detectives to conduct the investigation. It's generally a matter of integrity and I don't just mean people integrity I mean the integrity of the case.
I believe it is very common, if not entirely standard, for other law enforcement to be asked to conduct investigations in cases like this, to avoid any appearance of impropriety or partiality. In most states, it would be the state police doing it.