Before this new breed of pistol was invented a DA had to trigger cock the hammer against the force of the mainspring.
Agreed, the mainspring is indeed under tension. However if the hammer is UNCOCKED then one must press the trigger to cock and drop the hammer (to fire in DA mode). The mechanical shock required to ignite the primer can only be delivered by a fully cocked hammer. Therefore it is simply DA. The amount of trigger pressure may be reduced but the hammer MUST be cocked to deliver adequate mechanical energy, either manually or by operation of the slide or by pressing the trigger - just like any other DA pistol.
Restrike capability is defined correctly in the blurb you quoted.
I described restrike capability as marketing nonsense. That's it. I didn't re-define it. The term "restrike capability" is used in the defense pistol industry and it's presented as an advantage when it's not. If the gun doesn't go bang with the trigger is pressed then the problem is more likely something other than a misfire (empty chamber, failure to feed, unseated magazine, failure to eject). It encourages a user to keep pressing the trigger in the hopes that the gun will eventually fire, instead of taking immediate, positive action to get the gun back up and running. Hence "marketing nonsense."
For example, the M4 carbine doesn't have restrike capability. Neither does the 1911A1.
As you already know, not all the guns mentioned in the blurb you quoted have a trigger that will cock the striker/hammer, in fact most of them will not do so. As you know, most of the guns listed require the slide to tension or partially tension the mainspring before the trigger will do anything at all. And you know that's not the way a true DA or DAO behaves because you stated correctly that a DA or DAO has a trigger that cocks and drops the striker hammer.
This is how Glock describes their trigger mechanism:
"The “Safe Action” system is a partly tensioned firing pin lock, which is moved further back by the trigger bar when the trigger is pulled.
"When the trigger is pulled, 3 safety features are automatically deactivated one after another. When doing so, the trigger bar is deflected downward by the connector and the firing pin is released under full load. When the trigger is released, all three safety features re-engage and the GLOCK pistol is automatically secured again."
Pressing the trigger cocks and drops the striker. Period. The striker obviously cannot be manually or automatically cocked to operate in SA mode.
Operating the slide merely resets the trigger mechanism, which requires tension to maintain positive contact to ensure positive operation. The fact that the striker is "pre-tensioned" does not make it different from any other DAO auto pistol. Press the trigger and it cocks and drops the striker. It does not fire from the "pre-tensioned" position alone otherwise there'd be no need to retract it to "full load" position by pressing the trigger.
(If it were capable of firing from the "pre-tensioned" position alone then it would be an SA mechanism like the 1911A1.)
A Beretta 96SF can be fired, in DA mode, with the hammer in half-cock (i.e., "pre-tensioned"). Should new terminology be invented to describe this ordinary DA trigger function? Install a factory DAO 92D mainspring and one can convert it into a Beretta 96LDA!
How much trigger pressure required is irrelevant - if you press the trigger and the hammer or striker moves backward, then the trigger mechanism is either DA or DAO.
The purpose of marketing is to convince you that product features are unique and superior to competing products.