NonLiving trait ONLY grants Finite Life and Poison Immune to creatures.
If the creature is non living and doesn't specify Psy-Immunty, it doesn't have it.
[mwcard=FWC08]Invisible Stalker[/mwcard] is not Psyi-Immune
[mwcard=MWSTX2FFC10]Sardonyx, Blight of the Living[/mwcard] is
Skeletons, Zombies and so on have Psychic Immunity specifically stamped on them because non-living doesn't imply it.
This becomes tricky or at least easy to gloss over, because a psychic effect can just call for "living creature" in its target anyway, like [mwcard=MW1I26]Sleep[/mwcard] for example.
but, some spells like: [mwcard=FWE01]Charm[/mwcard] [mwcard=FWE07]Mind Control[/mwcard] [mwcard=FWE08]Mind Shield[/mwcard] are all psychic in subtuype, but can be cast on non-living creatures who aren't immune. The same is true for attacks from a creature like Psylok or Screeching Harpy.