You are right, Stirlings are not IC (Internal Combustion) since the heatsource is outside the engine it selves. Neither are they to put into the category of steam engines since they don't invoke a phase change vapor <> liquid. If to be categorized I would put them among “hot air engines”, sealed devices that work trough the Carnough cycle without having the media (air, helium, whatever) to go trough a phase shift (liquid <> gas).
But I guess that cnczone isn’t the right forum for this. Try Model Engineer.
Best regards from Sweden, the country of the midnight sun