This is the 12065th most frequent Russian word.
играм
"Играм" is the dative plural form of "игра" (game), meaning "to the games" or "for the games."
The word 'играм' is in the dative plural form, indicating the indirect object of the verb 'участвую' and referring to the games.
Я часто участвую в интеллектуальным играм.
I often participate in intellectual games.
Here, 'играм' is also in the dative plural form and indicates the object for which the packaging is prepared.
Детям нравится видеть красивую упаковку к играм.
Children like to see beautiful packaging for games.
In this sentence, 'играм' serves as the object of focus in the dative plural form.