The other major thing you'd have to tweak for your own setting is the Icons. The good thing is that although the game makes heavy use of the Icons, they are themselves referred to in generic terms; the game refers to the "Lich King" but this could be Vecna, Azalin, Nagash, Sauron or Skeletor. It needn't even be a lich king if you didn't want it to be; there's an article on Rob Heinsoo's blog about using 13th Age to run a Shadowrun game and using corporations in place of Icons.
Now I have this bonkers idea -- bonkers because there's no way my group would play it -- to run a Masters of the Universe campaign using 13th Age. There are a couple of approaches one can take with adapting a setting to 13th Age and its Icons; in some cases a straight swap might be possible, but I don't think there's any harm in coming up with new roles if the standard ones don't fit without becoming meaningless.
Skeletor is an easy one, because of course he's the Lich King, a fallen skull-faced wizard desperate to discover the Sorceress' secrets and conquer Eternia. He is allied with or opposed to Hordak depending on the day of the week and has a mysterious connection to the Eternian Royal Family.
The Sorceress is a magician allied with the Royal Family, but is also somewhat aloof and has her own agenda. She could be a straight swap for the Archmage or the Priestess, but I'd probably lean towards the Archmage to make her a bit more unpredictable.
Hordak is a cyborg skeletal pig man with an army of robots and a bat fetish, so isn't a neat fit with any of the existing 13th Age Icons and I'd probably create a new role for him, opposed to the Royal Family and allied -- sometimes -- with Skeletor. He's also stuck on another planet most of the time, and that's an interesting contrast with the more active Icons.
The Eternian Royal Family fit well in the Emperor role, standing for civilisation and order in a chaotic world. As such, King Randor and Queen Marlena have much in common with the Sorceress as they all strive to keep the world safe. As an extra complication, the Queen knows that her son is also the Sorceress' champion He-Man, but Randor does not, because he's a Dad and Dads are rubbish at knowing what's going on with their kids.
King Hiss would seem to be a good fit for the Orc Lord role, an ancient force of chaos and destruction returned to the world and seeking to overturn civilisation. He works with Skeletor or Hordak in rare circumstances but the alliances soon break due to mutual distrust. Although Hiss does not know the Sorceress, her magic is the same as that which banished him aeons ago so he considers her an enemy.
Zodac is another who doesn't fit in with the standard 13th Age Icons as he's concerned with balance and neutrality. The closest 13th Age gets to that is the High Druid, but she's all woodcraft and lentils and Zodac's more ray guns and floating chairs and ripping off Jack Kirby. Neutral alignments can be a bit naff in D&D but I think that the way 13th Age makes alignment more a matter of association with actual personalities gives neutrality more potential; it's difficult to play a character who strives to maintain a balance between abstract moral concepts but it's easier when those concepts are embodied in other characters with their own personalities and goals. So Zodac is in, as an observer and secretive manipulator of the other Icons.
There's one notable omission up there. I've left out He-Man because while he is somewhat iconic -- what with his name being in the title of the cartoon and everything -- he doesn't seem to be much of an independent operator with his own goals; rather he serves either the Sorceress or the Royal Family, or both. I suppose one could create a role for him but it doesn't seem in keeping for Icons to be subservient to each other and as much as he is the most powerful man in the universe, he is also a bit of a lackey. Also, with He-Man off stage it means that there is more for the players to do.
I've also stopped at six Icons, in part because the setting is not quite rich enough to support the full thirteen, but also because I suspect 13th Age's Icon system is flexible enough to work with a lesser number and all this nostalgic waffling is -- in a way -- supposed to be a proof of concept.
Now all I need is for someone to play it.