Let's see if I get this right
The game's heroine has multiple love interests as indicated by the cover. This new guy is supposed to be one of them. As part of the generic backstory and gimmick the otome love interests have, this guy's gimmick is that he's engaged to the villainess (Elizabeth). When he falls in love with the game heroine, he will inevitably break his engagement with the villainess and fall in love with the heroine. Hence the title, engagement breaking prince. It's a common otome event. That's according to the game.
In the game, Elizabeth gets banished for being the villainess who bullied the heroine. In this story however, Elizabeth is kind but still gets banished after being framed by the heroine. It's as if the world is forced to move according to the game's plot.
The heroine in this story however chose none of the love interests in the cover and went for the secret route. Which means this guy doesn't get together with the heroine so he's still technically engaged with the villainess (Elizabeth). Time has passed from the events of the game and the heroine already got married so Elizabeth thought everything was over. Which is why she wondered if "the story no longer controls us?"
All the supposed love interests of the heroine still exist even after she got her ending. This guy is a leftover aspect of the game.