The most glaring example I can think of is Final Fantasy X. I would put things in spoilers, but honestly, the game has been out for >10 years.

The main character Tidus begins the game in a technocratic civilization called Zanarkand, where he's the closest thing to a prince. They have a sport called blitzball that they basically treat as a state religion, and he is its star player. At the beginning of the game, the civilization is destroyed and he is transported to Spira, the society that inherits the world after Zanarkand is destroyed.

The game centers around this enormous monster called Sin that roams the world destroying cities that must be (temporarily) killed every 20-30 years for there to be any peace. In order for it to be put down, a summoner must sacrifice his/her self. Tidus ends up escorting and falling in love with a serene female summoner named Yuna, who's a stand-in for Anthy.

The Utena-like part comes in when they reveal the origin and nature Tidus and the monster Sin. It turns out that the nation Zanarkand was in a Cold-War type scenario with another nation called Bevelle. Zanarkand used summoning magic, Bevelle used technology. Zanarkand summons Sin knowing that Sin will destroy both Zanarkand and Bevelle. To preserve Zanarkand in some form after the destruction of their civilizations, Zanarkand's summoners create a spiritual clone of the city and implant it inside Sin, making it the spiritual and physical heart of Sin, its "reactor." Tidus isn't a person; rather, he's a citizen of Sin-Zanarkand, a dream of a dead civilization made flesh. He's its lost prince, its ideals collected and personified. He also finds out that there is a way that Sin can be destroyed once and for all, and that this final destruction doesn't involve Yuna sacrificing herself. It does, however, require him to allow himself, along with the eternal dream of the fallen empire of Zanarkand, to finally die. He allows both himself and the dream of Zanarkand to dissolve, and Sin dies once and for all.

The sequel involves Yuna/Anthy going out to find a way to bring Tidus/Utena back. If you follow some VERY SPECIFIC steps, you succeed. This only reinforces the FFX/SKU correspondence.