  The Willmore energy plays a central role in the conformal geometry of
surfaces in the conformal 3-sphere \(S^3\). It also arises as the leading term
in variational problems ranging from black holes, to elasticity, and cell
biology. In the computational setting a discrete version of the Willmore energy
is desired. Ideally it should have the same symmetries as the smooth
formulation. Such a M\"obius invariant discrete Willmore energy for simplicial
surfaces was introduced by Bobenko.
  In the present paper we provide a new geometric interpretation of the
discrete energy as the curvature of a rolling spheres connection in analogy to
the smooth setting where the curvature of a connection induced by the mean
curvature sphere congruence gives the Willmore integrand. We also show that the
use of a particular projective quaternionic representation of all relevant
quantities gives clear geometric interpretations which are manifestly M\"obius
invariant.
