It's not weird to me either.
I played the first Shadow Hearts but I don't remember getting very far because I think it scared me too much! Lol I kind of want to pick up this one, to see what it's like.
But guys, it is a video game. From Japan, no less. They make characters with big eyes and unusual hair with unique clothes designs. The game is not about Anastasia though, but I doubt they care about being historically correct. It is a fantasy game, with magic and monsters.
Here is also a description of her for the game:
Princess Anastasia Romanov: Outgoing and inquisitive, Anastasia is suspicious of her father's adviser, Grigori Rasputin. When he frames Yuri and party for controlling Anastasia, and almost forcing her to murder her little brother, Alexei, she joins Yuri to stop Rasputin. She uses a special camera to take Snapshots of creatures, capturing their abilities, some of which she can then pull from her Album to use in battle herself. She does physical attacks with mechanical Fabrage eggs.