"When the White Tower falls" could be referring to when the Thalmor took the Imperial City. Then again, probably not, as that line should be referring to the events of TES4.
Not merely to the events of TES4, but to the breaking of the Pact of Alessia with Akatosh, which was really the culmination of what happened in Oblivion. White-Gold symbolized that pact and now it's rendered powerless. I get the impression that while the Statue of Akatosh performs the same functions as a Tower (that is, anchoring Nirn to the Mundus and thus keeping it seperate from Oblivion), the fact that the Pact itself is broken (Which was really Dagon's and the Mythic Dawn's ultimate goal when you get down to it; as so long as that Pact is there, Akatosh cannot eat the current kalpa to begin a new one, freeing Dagon from himself) is a big reason behind exactly why Akatosh-Alduin is doing his thing in Skyrim.
When you get down to it, if belief is power on Nirn (which is why the Pact of Alessia had the power it did), what Akatosh really was trying to
do with that whole thing was gain enough
belief that, post Lorkhan's "betrayal", he could eat the world, freeing himself again from Lorkhan's machinations. That Alessia found the whole "Akatosh" thing as a midpoint between Shor and Auriel is a convenience that both found beneficial. It was a mutually agreeable thing at the time, but now, Akatosh no longer
needs it.
Akatosh and Alduin are aspects of the same being; one of Linear time and one of Cyclical. With these events manifest, they are served as one.
I kind of went off on a tangent there, but essentially what I'm trying to say is the Book of the Dragonborn confirms a lot of things I've long suspected.