Now you've got a different relationship, because before players could have only one team, but they can have many games and also belong to many games.
So in Game you add
and in Player you add
For this type of relationship neither your games table nor your players table gets a foreign key. (In the Teams-Players question the players table had a team_id column).
So you have to create a third table to allow rails to manage the relationship. The name of the table should be the two other tables in alphabetical order, separated by an underscore.
So in this case, that table is named games_players, and contains a game_id column and a player_id column.
Now a player magically has an array called games, and a game has an array called players. To add a player to a game, write it like this: some_game.players << this_player. Or you can do it the other way around. It doesn't matter, because what will happen is that rails will add to that join table a row containing both IDs.
But this is just scratching the surface. There is much more you can do with a HABTM relationship. Googling has_and_belongs_to_many will get you a whole bunch of good articles.
Also, if you still have teams that part doesn't change. A player can both belongs_to :team and has_and_belongs_to_many :games.