@Aoixneko I was told recently that such villainess characters rarely exist in modern otome games, though they might have been more popular characters in the past, in old games. So, while technically all of these numerous manga series, where the FMC is the villainess, could refer to old games, I now reckon it's just a trope that the authors are following, without necessarily having much to do with how the games actually are. So, if you happen to try a random, not so old and dusty otome game, chances seem to be that there won't be a villainess rival character in the first place.
Still, this isn't fisthand information from me, so take it with pinch of villainess-esque poisoned salt.