How to delete duplicates in SQL table based on multiple fields

You can try such query:

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 leave in database only one example of each game instance which has the smallest id.

You should be able to do a correlated subquery to delete the data. Find all rows that are duplicates and delete all but the one with the smallest id. For MYSQL, an inner join (functional equivalent of EXISTS) needs to be used, like so:

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 delete games from games with select * from games. Don't just run a delete on your DB :-)