It is one of those mysteries of life that is hard to explain, without the assistance of some really good clinical research. Adults like to play, and children need to play. It is even better when children play with adults and adults play with children. Science has proven that play is good for both children and adults, and most of all, it is fun!
It is easy to understand that both children and adults learn from play. However, there is more going on than meets the eye. Different ages of children play for different reasons, which means play like everything else in one's life is developmental. The more one develops the more complex the need becomes. Like most other skills in life, the developmental process does not preclude the previous skill sets. It is a little bit like basic math, everything that comes next builds on what you already know.
However, one of the most important things to remember is that developmental processes only go one direction. A person can get better at anything they have already completed. But they cannot begin or comprehend the process that is beyond their age appropriate educational level or experience level. A baby should never be expected to interact successfully with a school-age sibling, unless the school-age sibling is willing to play at the level of the baby. Unfortunately, adults sometimes think that a child with verbal skills is ready for adult like play when they are actually only ready to continue their development at the level they have skillfully reached.
It is up to the adult to make sure that the child has ample opportunity to play at the appropriate developmental level. It is one of the fundamental laws of nature that the organism with the most skills must accommodate the organism with lesser skills. This is true of adults with children as well as adults with other adults.
When adults play with adults, whether it is in organized sports or at a meal with friends, the developmental process began as a child continues. Skills improve, and people develop.