You can try a query like this:

DELETE FROM table_name AS t1
WHERE EXISTS (
 SELECT 1 FROM table_name AS t2 
 WHERE t2.date = t1.date 
 AND t2.time = t1.time 
 AND t2.hometeam_id = t1.hometeam_id 
 AND t2.awayteam_id = t1.awayteam_id 
 AND t2.locationcity = t1.locationcity 
 AND t2.id > t1.id )

This will keep only one example of each game instance with the smallest ID in the database.

You should be able to perform a correlated subquery to remove the data. Find all duplicate rows and delete all but the row with the smallest id. For MYSQL, you need to use inner joins (equivalent to the functionality of EXISTS), as follows:

delete games from games inner join 
    (select  min(id) minid, date, time,
             hometeam_id, awayteam_id, locationcity, locationstate
     from games 
     group by date, time, hometeam_id, 
              awayteam_id, locationcity, locationstate
     having count(1) > 1) as duplicates
   on (duplicates.date = games.date
   and duplicates.time = games.time
   and duplicates.hometeam_id = games.hometeam_id
   and duplicates.awayteam_id = games.awayteam_id
   and duplicates.locationcity = games.locationcity
   and duplicates.locationstate = games.locationstate
   and duplicates.minid <> games.id)

To test, replace remove game from game with select from game*. Don't just run delete on the database :-)