I believe they do, because IMO there is no reason not to.
That's not really good enough. Because there's no reason to have them, either. When the exact same argument fits both possibilities, that argument doesn't really give you anything.
Consider dwarves. "Forged by Moradin" could be their mythology for their god creating them. Nothing says Moradin didn't use genes and science (i.e. magic or god-like power or whatever) to "forge" them.
The minotaur. A curse, certainly, in a world of magic. Nothing says the curse can't manipulate the genes and mutate them, just like how mutation happens with superheroes or even things in the real world.
So, does a fantasy world need genetics? Of course not, it's magic, after all, but IMO I see no reason not to have genes, DNA, etc. In the same line, it is why there is still gravity. Does "magic" make things fall down??? Probably not, but you could say so if you wanted, its your world.![]()
But, really, there is a reason to not have genes and such in your fantasy world. That reason is that words mean things. The terms "gene" and "DNA" bring with them a significant number of assumptions about how the world works. That sets expectations of how the world works in the player's minds.
Are you bothering in the least to actually follow those expectations? No? Then don't set them. There is no reason to do so.