Colorful "parachutes" are used for various kinds of pre-school games. The parachute, in this context is a large (many feet in diameter), strong, circular cloth, usually with handles around the edges. Typically, it is completely unfurled on or parallel to the floor, and players stand around its circumference and hold it up by its edges. Then, they collectively manipulate it, to raise and lower it, to make waves in it, to make the center descend and pop up, etc. Some games include some or all players going underneath the unfurled parachute; in many of these games, the parachute is referred to as a "tent."
I am wondering whether parachute games, as described above, particularly the ones that involve going under it as a "tent," are permitted on Shabbat. It certainly sounds a lot like "building a tent," which is one of the activities prototypically banned under the category of Boneh (Building). Halachipedia says:
It’s forbidden to set up the roof of a tent, permanent or temporary, on Shabbat, even if one there are no walls. ... (Shemirat Shabbat KeHilchata 24:1-2)
It is forbidden to set up a tent out of blankets even if it is meant to be temporary. (Menuchat Ahava vol 3, 23:8, Shemirat Shabbat KeHilchata 24:1-2)
Footnotes imported and enhanced with links for presentation here.
On the other hand, the only supports used for this "tent" are people, and the structure is inherently temporary. I don't know whether these mitigations matter in this context.
Are parachute games, in general, permitted on Shabbat?
Does it matter if people are going underneath or not?