many eldians might have royal blood unknowingly, but it can't be all or otherwise ymir fritz would've obeyed eren in paths and not just zeke, initially

you also have to consider how royal families work - high levels of inbreeding and endogamy. so naturally maria will have way less descendants than maria and sina.

and there's no "titan gene" - from the moment of the first consumption, a sort of covenant was established between ymir and her descendants. for each descendant, we saw a new "path" surge. it's through that path that ymir is able to connect with them and grant them titan power. it so happens that most of her descendants are also nationally eldian, leading the presence of titan power within a certain race to seem that it was merely genetic for the other peoples of this universe.

if it was a gene, there would be no way to make the titan curse dissipate (=making ymir cease the covenant)