Ever since I watched the Dark Side of Dimensions movie, I always wandered about how Kaiba was able to summon Obelisk in his duel with Diva, since the god card were supposed to be lost after the Ceremonial Duel. I don’t think this is a theory, but an explanation of what the movie and anime says. (Japanese of course)
Now, when we’re first introduced to Kaiba’s new Duel Disk, this is the description we get.
I’m not all that good with physics and technological-terms, but from what I can understand, Kaiba no longer needs an actual card, cause he has the card data from all over the world, but his brain as well.
Now, let’s go to when he actually is about to summon Obelisk.
He clearly states that since he failed to defeat him in a duel, his “ghost” continues to wander, which I interpret as that he still remembers him.
Now when he actually does summon Obelisk, this is the reaction we get from Diva.
A bit hard to understand? Kind of, but in simple English it just says that while Kaiba was in that sacred domain (aka the temple/resting place of the Millennium Items/door to the afterlife)he was able to somehow communicate with Atem’s spirit and therefore, summoned Obelisk, his mightiest servant. Let’s not forget that only those that bare a Millenium Item or are chosen by them or are connected to ancient Egypt can summon an Egyptian God.
Even in the anime, Kaiba always seemed to be the exception, without even Ishizu fully understanding how he wielded it in the first place.
So, to get to my point, being able to wield a God Card to start with, being in that sacred place in DSoD, allowed Kaiba to recover and summon an Egyptian God Card.