It sounds like the same song different verse from almost 2 weeks ago involving your ex's new husband taking on the role of step-father remember you didn't want him to transport the children, you wanted to do it. Yet you say you are happy for her and for your children that he is good to them. You said, "I am very lucky to have a new husband/step-father for the girls who treat them so nice. "
So you acknowledge he has taken on the role of, step-father, you are still their father and their "Daddy" and that will never change. The role of step-father, is different yet one does not normally call their step-father, "step-father" but what can they call him that won't hurt your feelings? There are any number of names that can be used, you are still their father and their "Daddy" they are not changing that. "Dad is distinctively different, would you object to "Pop"? Children will pretty much do as they want and even make up names that they use on their own, especially once they get older.
When I got married, I called my in-laws Mom and Dad, out of respect, not because of how they treated me or how I felt about them, I also hugged them as a matter of routine as that was their manner of leavetaking not because it was mine, at least I was short enough that I wasn't forced to kiss them good-bye as well.
My grand daughter made up her own names for people, as an infant my son was her primary cargiver because her mother was deployed for 6 months when she was 6 months old, her DADDY was the one and only in her eyes, other men were called daddy same word different inflection and different level of trust and she knew they were different than Mommies because she didn't have any other words. One day she even called me DADDY what an honor! She also, had 3 grandmothers with the same first name, both maternal and paternal grand mothers and a great grand mother all had the first name, what to do? At first the parents decided different names, I became without any say so, "Nana Bear" a few years later, she decided one day to start calling me, "Grannie" I prefered Nana Bear to Grannie, but I said nothing, she now calls me Grandma.
Your children will eventually do what feels comfortable, think of it as a showing of respect rather than something to take away from your role, you will always be their father and if they are fortunate to have a good relationship with their step-father then they are twice blessed.