I disagree with that definition.Any speaker with a coil attached to a paper cone, where the magnetic core is inserted into the coil (paper-sleeve bearing may exist from the cone), is by definition an inductor.
Of course it has inductance but that doesn't mean you define it primarily as an inductor.
A speaker is more a linear motor as Colin55 stated.
Motors do have inductance but they are not normally called inductors.
The word "inductor" is typically only used for devices that are purposely designed to have inductance, not where the inductance is incidental to the design..