Not quite? The Great Darkness is strictly "thinking about itself, forever, and consumes all other consciousness into thinking about itself". The example in the video is subsuming the universe into consciousness but NOT just to think about itself. Kinda-sorta like the Borg--it assimilates, but it does not just think about itself.
The Shivans get by by A) not centralizing its intelligence and thus keeping its consciousness too disjointed and separate to be vulnerable, B) using an inherently destructive thought process, thus actively countering "think about me" attacks because any such thought gets attacked and destroyed immediately by all other thoughts, and C) not thinking far ahead or planning ahead, thus not needing centralized intelligence or constant high-level thought processes which could be vulnerable to "think about mes".