Let me help you guys out to finish this debate.
appliance
definition:
a device or piece of equipment designed to perform a specific task.
Therefore the new Mac Pro is an appliance. The old Mac Pro is also an appliance. Every computer is an appliance.
The key word in your definition is "specific". Most workstations are designed to be flexible and to be applied to many different tasks from mathematical theorem proving to video editing. They are therefore not appliances according to your definition.
The new mac pro is closer to being an appliance as it is designed primarily for video editing.