#[derive(Default)]
struct GameState {
    board: [XorO; 9],
}

And then you actually don't need the function GameState::new() but can call GameState::default() instead to create a new instance of GameState.

The functions print_cell and show_board can be substituted with a std::fmt::Display implementation. The print_cell could then look something like this (not tested):

impl std::fmt::Display for XorO {
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        match self {
            XorO::X => write!(f, "X"),
            XorO::O => write!(f, "O"),
            XorO::Empty => write!(f, "."),
        }
    }
}

You can then print out XorO by simply doing println!("{}", XorO::X)