“No way — where’s the fire that all firearms produce to expel the bullet?”
One of the definitions for the intransitive verb “to fire” is:
to emit or let fly an object (Merriam-Webster)
Such dictionary definitions to do require any combustion for the verb to mean the propulsion of an object by whatever means. The method of propulsion with a BB gun may be either a spring or compressed air, which does in fact “let fly an object” as described in the definition.
Get real.