Congratulations, you've found yet another bug in MySQL (that isn't likely to get fixed, because to the MySQL developers, it's not a bug, it's a feature...)
Normally, in a RDBMs, a select statement like this:
select dept, enum from phonebook_main group by dept;
You'll get an error (like the Spec says you should) of:
ERROR: Attribute phonebook_main.enum must be GROUPed or used in an aggregate function
Since you want a sum of noofgames, just do use an aggregate function sum() like so:
SELECT bowlername, sum(noofgame) FROM ".$score." GROUP BY bowlername