This game is about something specific: the rise of a character from rich but somewhat humble origins to greatness at the cost of those things most dear to him. Its focus has nothing to do with genre, so as long as the genre supports characters with deep, personal connections to things they stand to lose and a rise in greatness, it works.
In messing around with the rule set, I've seen the following potential alternate takes:
- Swashbuckling - I'm running 7th Sea right now, so of course I'd drift here first, but it does follow. Swashbuckling is a genre of high action and romance. There can be plenty of epic struggle here, and heroes rising up against a corrupt political power is very much in line with this genre. The romantic aspect of the genre sits well with the hope mechanics in this game, though stories told with this system may have a greater tragic element than in other games.
- Westerns - As a genre, at least in the movies, Westerns often involve rough characters who have some pretty ambiguous morals. Certainly that's the realm of the spaghetti western and The Man with No Name Eastwood portrayed so many times. However, more modern takes on the genre sprinkle in a hefty dose of heroism too. Look at Tombstone or 7:10 to Yuma. If everyone at the table establishes that this is the sort of western they're going to play, Heroes of Destiny is a good fit.
- Supers - The base mechanics would need some adjustment in order to deal with the increased level of power present in a supers game, but it's certainly possible to handle such stories in this game, with one big caveat. Superhero stories, at least as shown to us in the comics, tend to be static. Yeah, things do change over time, but how long did it take Lois to finally discover Superman's identity? When's the last time a major hero died and stayed dead? Things have a way of returning to the status quo pretty regularly in the comic book world, and that's not the kind of story that this game is designed to tell. However, within comic history there are a number of isolated arcs that, if taken out of the larger flow before later issues reversed them, serve as great examples of the kind of superhero tale perfect for this game. Look at Spider-man and the Green Goblin when he accidentally killed Gwen Stacey. Look at the Doomsday rampage, or No Man's Land. Stories which really push the hero to the limits and put at risk everything he holds dear are perfect for this, as long as the campaign doesn't later undo any big changes. The big difference here is that Heroes of Destiny is designed to ultimately come to an end. comic book stories aren't.
- Space Opera - Given that space opera is really just fantasy in different clothes, there's absolutely no reason to think that this game would have difficulty in dealing with the genre. You'd need some rules for ranged weapons, assuming you're not comfortable reskinning bows as blasters, and there should probably be some vehicle rules too, but outside of that, it's almost good to go out of the box.