A "special livestream" refers to a live video broadcast that is different or unique from regular livestreams. It may showcase something out of the ordinary, like a special event, exclusive announcement, or a one-time performance. Full definition
This Wednesday, Entrepreneur will broadcast one such conversation in a special livestream right on this site. (entrepreneur.com)
Dragon Quest XI is indeed for a home console — the PS4 — but it's still multiplatform, as it will also come to the 3DS, Square Enix revealed during a special livestreamed event just moments ago. (playstationlifestyle.net)
Today, Atlus held a special livestream dedicated to the Shin Megami Tensei series on NicoNico. (perfectly-nintendo.com)