Sice gêm is a feminine noun (and singular), shouldn't it be written "yr êm" with a soft mutation and a different article? Maybe the mutation depends on which vowel follows the consonant, in addition to word gender and number.
This is one of the rare exceptions where the feminine noun doesn't mutate after the definite article. This usually affects loan words from English.
The appropriate form of the adjective is still necessary though:-
Y gêm fawr, Y gêm dda etc