Physical play is how DD connected with other kids when she was younger. They might not really be friends in a broader sense, but they had their game in common. My favorite game for crossing all kinds of boundaries between kids (age, skill level, intellect) is Calvin Ball! I taught her and she taught her friends.

http://en.wikipedia.org/wiki/Calvin_and_Hobbes#Calvinball
http://pandeia.eu/wp-content/uploads/2014/06/Calvinball1.gif