Add two buttons to allow the player to choose a team to join

This demonstrates how a "Join Team" button could actually work.

Of course, the notion of teams and being able to switch from one to
the other is a bit much for tic tac toe, (but could actually be useful
for a case of two people playing on a single computer for example).

What we definitely want here is some implicit team membership. Such as
"Either play can make the first move" and then having that assign the
player that moves to Team X.

If we did that, then we could also simplify by having just a single
"Swith Teams" button instead of having one button for each team.