There was a recent Jackie Chan movie with this theme.

Anyway, I'll wager you've never had any significant dance
lessons or studied martial arts.

Your idea fails to appreciate the enormous complexity,
variation, and nuances possible with regard to movement of the
human body. Consider all the possible degrees of freedom and
range of motion in the arm: shoulder, elbow, wrist, finger
joints; the leg: hip, knee, ankle, toes; add the waist and
neck; and no doubt there's more I've missed. In addition,
there's more to dancing than just the raw movement -- there
are underlying principles, both practical and artistic, that
drive the expressive nature of the art. Dancing is NOT just
going through the motions.

You admit your system would require training in order to
develop the correct response to the stimuli, however the
"language" you envision would be have to be so complicated in
order to cover the full range of possible movements, that
learning it would negate any advantage over being taught by
traditional methods. Indeed, we are naturally "wired" to
learn by imitation, which is why that is a more effective
means to teach dance moves than your proposed simuli. All
you are proposing is substituting one skill for another --
i.e., replacing dancing ability with responding to pokes --
and that new skill can in no way adequately replace the old
one.

It's possible that for a smaller subset of movements, your
system might make possible a limited kind of sychronized dance
for unskilled groups. But there's no way it could be used to
for complex dances or to train professionals. Watch some of
the ballroom dance programs on PBS -- the level of expression
and complexity required makes it out of the question.