The slingshot was crucial to the story

SPOILERS:

Madec checks over the dead miner's cave residence to make sure there's nothing available that Billy can use. But Madec doesn't see the wrist-braced slingshot in a niche at the back wall. Billy sees it, though. Madec's mistake is ultimately his undoing near the movie's end. Billy uses the slingshot to incapacitate Madec.

The slingshot proves itself as a viable, last-ditch defensive weapon. No common-sense man would select a slingshot over a reliable revolver for home defense. But what if you did not want to own a firearm? Or what would you do if you lived in a state where you cannot carry a handgun in your backpack while hiking, camping, or fishing? Imagine being confronted by a wild animal like a mountain lion. I won't discuss the obvious, a bear, for which a heavy firearm would be needed for self-defense. Imagine a threatening criminal who is built like a bear, and holding a non-firearm weapon like a club or a knife? If you could not run away, would you want to engage him in hand-to-hand combat or use a stand-off weapon like a slingshot? Just brandishing a loaded slingshot can show a potential attacker that you are not unarmed. You are armed with a projectile weapon that while usually not lethal can cause serious physical injury.
Had Billy not had the slingshot, he would not have been able to ambush Madec and incapacitate him with a slingshot.