In the strictest sense of the term, Glocks are indeed "DAO" pistols.
"Double Action" meaning that pulling the trigger does two separate things; one, it finishes cocking the striker, and two, it releases the striker.
But it isn't that simple.
You've
redefined "double action" from the more conventional definition which was "using the trigger to set and release the striker or hammer" to something subtly different: the trigger is now used to "
finish setting and releasing the striker."
Where'd that "
finish settting" come from? <grin>
I'll agree that with some DAO the slide must be jiggled to make a second trigger pull possible. But not all of them are that way. In most of them aren't.
The CZ 100, CZ75B DAO, SIG DAO models, including the new DAK trigger-equipped models, can all be fired by pulling the trigger again. They are TRUE DAO guns. As are many revolvers. The SA/DA guns can also be fired by pulling the trigger a second time, if the first pull doesn't work. Ditto DAO revolvers, and their DA/SA brethern.
But that's not true of a Glock.
I'd argue that if the Glock were a true DAO, you'd be able to fire it, ammo willing, by simply pulling the trigger again. But a Glock wont let you do it until you've moved the slide 3/8th of an inch or so.
With a SA gun, the striker or hammer spring must be "loaded" or compressed before it can be released by the hammer. That's true of a Luger. Its also true of a Glock. Yet nobody calls a Luger a DAO gun... The fact that a Glock must go a bit farther and load the spring a bit more doesn't change the fact that it wouldn't work if the slide hadn't already done most of the work.
As I said before, the Glock is neither fish nor fowl: it has traits of both a DAO gun and SA gun.