
No it wasn’t. He said it wasn’t unusual and that people didn’t like that him and his sister had a kid. Nothing about them being obligated to do it.
It would have been a more fucked up plot twist, though, the family grabbing the two teenage brother and sister, locking them in a bedroom and commanding them: “FUCK! Or you will be punished!!”

He said it was first done to keep royal blood pure, making it a rule that royal family (immediate or not) were to marry and have kids. As time went on, it just became custom to do so which is why he and his sister got together. No one locked them in a room but incest is all they know in terms of lineage.
Either way, obligated or not, yes the duke is officially tied to a child he had with his sister— not that unusual for the time period this is written in.
Still hoping the incest thing is some kinda of joke/code language between himself and his sister.
I don't want to believe the author is going to tie down the ML with a kid.