The phrase "special demo" refers to a demonstration or sample that is unique, different, or distinct from others. It usually showcases the noteworthy features or highlights of a particular product, service, or event. Full definition
Check with your local retailer during the holidays to find out about special demo code giveaways (while supplies last). (gamerassaultweekly.com)
It seems like Game Freak forgot to scrub the Pokémon Sun and Moon Special Demo of extra data, because it seems like we have the entirety of the Pokédex on hand now. (nintendofuse.com)
Pokémon Sun & Pokémon Moon Special Demo Version (Nintendo, Free available 10/18)-- It's hard to believe that we're just one month away from our next adventure in pocket monster collecting. (nintendowire.com)