Non-living (or sometimes unliving) is a term that refers to all creatures that are not considered to be alive. All non-living creatures have similar traits that typically somehow concerns a lack of "life force". For example, all non-living creatures are immune to Vampire Lords' life drain. The term non-living was officially introduced in Shadow of Death manual, where in the description of Elixir of Life (a combination artifact) stated that the artifact "does not work on Undead or non-living creatures". Although the description suggests that Undead would not be considered as non-living creatures, it is commonly acknowledged fact that Undead are also non-living beings. Additionally, Golems and Elementals are considered to be non-living creatures in Heroes of Might and Magic III.
Stone and Obsidian Gargoyles are also considered non-living, but they are still affected by morale and mind spells. What that means in practice is that they are not affected by Vampire Lords life drain and cannot be resurrected.