Power conditioner wire gauge? Serious issue

So I just figured out that all the 10 gauge wiring I have may be a problem if the power conditioner I use only uses 14 or 16 gauge wires to connect all those outlets you plug into in the back of those devices.

The specs are not part of the description when you buy Power conditioners.  Everybody recommends a dedicated 10 gauge wire from the panel but fails to consider what power conditioners use. 
 

Is this a serious problem?