How does " Sparsity of connections" in CNNs causes the network to have less parameters?
In fact these involve different aspects of parameters in a CNN.

Parameter sharing, means one parameter may be shared by more than one input/connection. So this reduces total amount of independent parameters. Parameters shared are non-zero.
Sparsity of connections means that some parameters are simply missing (ie are zero), nothing to do with sharing same non-zero parameter. Parameters in this case are zero, ignored. That means that not necessarily all (potential) inputs to a layer are actually connected to that layer, only some of them, rest are ignored. Thus sparsity of connections.