Play hones reflexes. Its entire purpose is to train young animals on tactics, and on how to use their body, and on their local environment.
Put another way, if you aren't trained to use your body, you're more likely to die. The same goes with not learning tactics. Or what the local environment is like.
If you don't know what a tree is, if you don't know what a hole in the ground is, what a hill is, how well grass hides you or not, you are at a major disadvantage, if you're hunting, OR if you're hunted!
There can be other mechanisms to learn things, but play is one of them, and having children teach each other, lets the adult protect, and gather food to feed. It also ensures that youth is trained up on the current environment, not one that the parent recalls from youth.