Otome is dating sim meant for girls where you play as a girl and try to get one of the male casts to like you. Opposite of Galge, dating sim for boy.

So when you are trying to romance a male char to like you, it should work like an otome than a galge, just minus any "female-only cutesy" action because those will just look ridiculous with a male char. You hang around them all the time, trying to know exactly what they're like and in the climax, use everything you know about the character to confront them and make the romance successful.

If anything, Red Prince works like those insanely hard to get character in otome game, ridiculously hard to get with a clear rival (Sadha) with also the weirdest flag to actually trigger his romance option and multiple way to lose him. The epilogue suck because you are given nothing but ways to lose him, including the slave option where he no longer views you as a romance option, just as a friend to joke around with.