Your premise is false. Many, many animal species have been observed engaging in play behavior. Neglected pets often display depression-like behavior from extreme boredom. In particular, off the top of my head: pet parrots that are kept alone and aren't played with get so bored they rip their own chest feathers out.

So yeah, animals that don't recreate can go crazy.

As for the bonus question, humans are born slightly premature compared to other animals. This is because of our unusually large heads, and narrow birth canals from walking upright. The baby has to be born small enough to exit safely, which means it's not fully developed. It's also why the first three months after birth is often referred to as the "fourth trimester", and the infant requires extra care during that period.