Do all systems in z domain are filters?
One way to think about this:

Everything that can be represented as a rational function in the Z-domain can also be represented as a linear difference equation in the time domain. As such at can be interpreted (and implemented) as a filter. It may be non-causal or unstable, but it's still a filter.

You can certainly represent things in the z-Domain that are NOT rational functions, however, that would be a system transfer function anymore, because the transfer function is only defined for LTI (Linear Time Invariant) Systems