OK, using the same table structure as the original poster, this appears to work. But, not sure if it is the most efficient.
SELECT *
FROM
(SELECT homeTeam.team_name as home_team, homeGames.all_games_id, home_goals, homeGames.date, homeGames.time
FROM teams AS homeTeam
LEFT JOIN all_games AS homeGames
ON homeTeam.team_id = homeGames.home_team) AS home
LEFT JOIN
(SELECT awayTeam.team_name as away_team, awayGames.all_games_id, awayGames.away_goals
FROM teams AS awayTeam
LEFT JOIN all_games AS awayGames
ON awayTeam.team_id = awayGames.away_team) AS away
ON home.all_games_id = away.all_games_id
ORDER BY home_team ASC, away_team ASC