Though people have tried, none have so far reached a definite conclusion as to what play actually is. If you want to read more I recommend the following books
The playful aspect is by far the most arbitrary. The word in itself is a bit silly. "The playful aspect of play". The playful aspect seems either obvious or superfluous. But since we've gone through the physical and social aspects, this last post addresses the parts of play that are harder to fit into the aforementioned "boxes". Between the physical and the social parts of playing, something else takes place as well...
Broken down, the social aspect of play is such an important part of any play-related activity. This is true for both play, games, sports, and any other event who has some sort of "play" in it. Admittedly, play doesn't have to be a social activity. You can play games (or freely) on your own. The social aspect however is still such a crucial part of most play, that it ought to be mentioned: It's a reason (Or a push) to get out, meet people, and be social on your own preferred terms.
The physical aspect of play is by far the most immediate aspect. When we play, be it a free-form of play or a more structured approach through games or sports, we use our body. Sometimes a lot, like when dancing, running, wrestling, or pretending to be dogs. Sometimes a little, like when playing chess or poker, where even the slightest movement of a facial muscle can be decoded into millions of meanings. The amount doesn't necessarily matter. Physicality is seen and interpreted by everyone, and is easy to relate to.
The magical circle is a little plane of existence that is both its own, and a part of our world. I like to call it the game world. Let's use my daughter playing with her friends as an example. From my perspective there are two kids rolling around on the living room floor, eating the uncooked pasta my daughter just got from the kitchen. From their perspective they are two dogs, a big-sister dog and a little-sister dog, and they are eating dinner they found outside their doghouse.