It's full of stuff like

    flipPlayer : Player -> Player
    flipPlayer currentPlayer =
        case currentPlayer of
            X ->
                O
    
            O ->
                X

which is 8 lines where idiomatic Haskell would take 3.

    flipPlayer : Player -> Player
    flipPlayer X = O
    flipPlayer O = X

I don't know if Elm encourages or mandates that verbose style but it's not some sort of "FP" requirement.