"Inspired" is most likely a past participle here because "inspired" describes the state of George Lucas after seeing the dog.
It could also have been a verb in a sentence in the passive voice. However, if it were a verb, the structure, in my opinion, would be
Director George Lucas was inspired to create the Wookiee character
Chewbacca—a “gentle, hairy, non-English-speaking co-pilot"—by (the act of) seeing
his wife’s dog sitting in the passenger seat of his car.
because, then, we could turn it into an active-voice sentence as follows.
Seeing his wife’s dog sitting in the passenger seat of his car
inspired Director George Lucas to create the Wookiee character
Chewbacca—a “gentle, hairy, non-English-speaking co-pilot."
Because that is not the case, "inspired" is a past participle.