Check winner in a Tic Tac Toe game
General advice:


Use enums instead of strings for board squares. This will protect you against mistakes like board[i] = "x".
A dictionary is overkill for a 3x3 board, you can just use an array. One benefit is that a bad index will throw an IndexOutOfRangeException, while a dictionary will not complain.
Board logic should be encapsulated in a class, so that you can make changes to your implementation (like switching from a dictionary to an array) without the rest of your code having to change. It will also allow you to guard against errors such as overwriting a non-empty board square.


To make the function easier to test:


Pass the board to the function, or make this a method of your Board class, instead of referring to GameBoard.Content.
Return an object representing the game state, instead of modifying private fields.


Together, it might look like this:

public static GameState GetGameState(Board board)
{
    foreach (var winningLine in WinningLines)
    {
        var line = new BoardState[]
        {
            board[winningLine[0]],
            board[winningLine[1]],
            board[winningLine[2]]
        };

        if (line.All(state =&gt; state == BoardState.Human))
        {
            return GameState.HumanWon(winningLine);
        }

        if (line.All(state =&gt; state == BoardState.Computer))
        {
            return GameState.ComputerWon(winningLine);
        }
    }

    return board.Any(state =&gt; state == BoardState.Empty)
        ? GameState.Unfinished
        : GameState.Tie;
}