One parallel that can be drawn from this newly confirmed information is that three of our main character's mothers died in childbirth...Dany, Tyrion, and now Jon. Could this be hinting they have even more in common? Maybe they are the three heads of the dragon?
Some people believe that it goes further than that and that Tyrion's father wasn't Tywin, but a Targaryan, specifically Aerys II (the Mad King), who lusted after Joanna (Tywin's wife).
The support for this theory is as follows:
1) Tyrion's stature could be the result of Targaryan inbreeding manifesting as dwarfism (and general ugliness from the book... Show Tyrion is an Adonis compared to Book Tyrion).
2) In the books, Tyrion's hair is much lighter than the show, apparently a pale whitish blonde. We all know that Targaryans have silvery hair.
3) Tyrion was able to get near Rhaegal and Viserion (the two dragons beneath the pyramid in Mereen) without getting roasted alive or eaten.