Yes, Otome is Leo’s cousin. I’m not sure how far her side of the family goes however, but that is indeed a fact.

However, that fact doesn’t really disqualify her from being one of Leo’s potential lovers in the game. In fact, she’s portrayed as the game’s main girl—the game’s default, poster girl in other words—the closest to the hero (along with Kani) from the get-go. I hear in Japan, marriages between first degree cousins are legal, as it’s also normal for a Japanese person to have grandparents who are in reality also cousins.