The sentences seem grammatically correct and clear to me, the most I could do is add same extra words? Is there something else that you had specifically in mind?
The ball game was very important to the Maya because with it, they were allowed to freely express themselves and their religious beliefs and practices. The Mayan people believed that through the game they were able to survive daily. To them it seemed as if in some ways, the game had allowed for the sun to shine, which in turn allowed for the people to harvest crops and get food. This was a huge part of their lives and they felt that without the game, they would die.
