That was an excellent chatter response.
Responsible usage of the rules tells us that a piece which takes only one
step ends its move after that one step and therefore is not eligible to
chatter. However, your idea sounds like a lot of fun!
One can always arbitrarily restrict Kings and Pawns from participating in
the fun; and I think this would be necessary, not only because it appears
to be too difficult to chase down a King supported by multiple riders (note
that 'a K supported by a Bishop' can only run towards the Bishop), but also
because the offensive uses of Chattering Pawns would dominate the game, as
they do in N-Relay II.
Decimal Chatter Chess, on a 10x10 board, would become quite interesting if
you had the Pawns on the third rank, all Riders on the first, and a second
rank full of weak steppers -- the usual suspects, W, F, Crab, Barc, A, and
D -- because the early play would be dominated by the weak pieces being
thrown forwards by the power of the riders. You'd need to arrange your
pieces very carefully, making room for the weak pieces to get past the
Pawns, setting up intersecting lines for the riders, and putting the
weakies where they could join in the fray but not get in the way. All the
while trying to maintain a defense against the pesky foe.