While he's a skilled hunter and resourceful, he doesn't find pleasure in violence or competition, which are the hallmarks of the Games. Instead, his involvement in the story stems from his:
* Survival: He hunts to feed his family and protect them from the hardships of life in District 12.
* Rebellion: He actively works against the Capitol, plotting to bring down the oppressive regime. He believes the Games are a tool of control, and he wants to see them abolished.
* Love for Katniss: His relationship with Katniss is a source of comfort and strength, motivating him to fight for a better future.
In essence, Gale's actions in the Hunger Games are motivated by survival, rebellion, and love. He doesn't "like" the Games, but he participates out of necessity and to create a better world for himself and his loved ones.