Gavra,
There is an issue of tiul that is brought down in the Terumas Hadeshen (and the Taz cites it) although it is unclear if the issue there is method of travel (shakey wagon) or the outing. But I would have said that this is an issue of schok that is certainly forbidden.
However, I have just discovered a Sh”v’T Davar Moshe that makes the exact chiluk you made and allows a couple to play ping-pong b’es niddasa.