With apologies to Wikipedia:
Parallel play is a concept from developmental psychology. It means mothers wiping off, feeding, sunscreening, locating, chasing, comforting, and/or punishing children side by side without interaction. It is commonly seen among mothers of children of ages 2 or 3 who only get to see each other once a year.
No further reports at this time as I'm still susceptible to the bends. (And actually, thanks to some very generous people, there was some group play as well!)