Vitality / "life force," the supernatural measure of how alive you are. It's the same thing that lets living shadows or fire elementals or a god be "alive" yet without biology as we know it.

The undead organism is dead, yet, through the Transference link, supernaturally alive. It's part of whole unnatural abominations upon Elanthia deal.

-Armifer
"In our days truth is taken to result from the effacing of the living man behind the mathematical structures that think themselves out in him, rather than he be thinking them." - Emmanuel Levinas

Poorly, since Quicken the Earth was a fairly late addition. The original material was not written with the idea that Necromancers could create non-undead constructs. As a rule of thumb, though: if an Empath can beat it with a stick, it doesn't have a life force and none of the conversation we're having about the undead strictly apply to it.

Conceptually, constructs were put in to serve two purposes. First, to provide a Necromancer summons that isn't quite as damning (literally and figuratively) as making Grandma a zombie. Second, to open the door to the idea of animating more exotic and non-traditional things, such as imbuing your enemy's sword with a mind of its own.

The "physics" behind how Necromancers are doing it and why it isn't producing a normal undead hasn't been fully explored.

-Armifer
"In our days truth is taken to result from the effacing of the living man behind the mathematical structures that think themselves out in him, rather than he be thinking them." - Emmanuel Levinas