Eh... May I conclude that Martin's transformation was an example of a powerful dragon shout? That even the last of the Septims had these abilities? If they were so powerful, why would they need such an extensive bodyguard as the Blades?
I think Thu'um is its own thing. The Dragonborn are able to perform Thu'um, the dragon shouts, with greater ease than others. But you don't have to be a dragonborn to use the shouts, nor are all dragonborn able to use them. In fact, except for the graybeards, it was considered a lost art. What Martin did was he shattered the Amulet, releasing the power contained within. I certainly didn't hear him yell anything like a dragon shout at least
In fact, it may be that the later emperors, the ones after the notable dragonborn ones, may not have been dragonborn themselves. That would warrant a name change of the Dragonguard to the Blades, if their primary objective of guarding the Dragonborn changed to guarding their descendants. It would also explain why the Septims in Oblivion were complete weaklings in combat, how each of the Emperor's sons were killed, the Emperor himself, and how Martin helped little in combat with his fancy set of armor and weak sword arm