The Author answered this on her tumblr :3 It's a gender neutral term in Thea's country. All legitimate children of the King are given the title of Prince.
Everyone visits this game even if it's probably never going to update (I hope it will tho) because it's so good that it deserves more attention. And we will give it the attention it deserves!
I think there is an error in the scene where you choose if you exited to see Arthur or that you hate him. I selected the one where I decided to hate him, and an error came.