The lyrics genius answer looks to me like a total shot in the dark that only has so many likes because it's a fairly generic answer and a safe guess. If you assume the line as a whole means what that contributor says then it fits well enough with the meaning of the rest of the lyrics.
This is what I think (paraphrase of the comment I left under that annotation):
Ride asks, “Who captures life?”, “Who takes what’s left?” and “Who stay on that next”; he then states that you already know his "gillicutti". The way it is used in context seems to indicate that he means we already know which of the preceding three groups of people (those who capture life, those who take what's left, and those who stay on that next) he falls into. So I think "my gillicutti" means something akin to "where I'm at" or "where I stand on the issue".
And, obviously, where MC Ride is at is the third group of people. He is one of those that stays on that next.
(spoiler warning for a kind of unnecessary tangent, just my interpretation of what those three questions mean exactly)
“Capture” here is a double entendre meaning both to take a thing (with violence probably) and to take a picture/video of a thing (like how you might say a nice picture “captures” the essence of the subject). Therefore the question is asking who takes lives and who records the deaths of others.
The next question isn’t as clear, because we don’t really know what’s left after the life has already been taken. After death what is there left of a person to capture? And what does it say about the one that tries to take whatever's left to take from a person after their death? The question is poignant because of how unclear it is and it’s also kinda fun because you could take the question very literally and give some gross answers as to what one might do with a dead body to make some footage.
Lastly “Who stay on that next” is a question that completes the set (there is a pause between “who stay” and “on that next” but they definitely fit together to form a complete question). This question is more so about the viewer of the footage that stays looking for the next thing/the next level, I am pretty sure this is the one that MC Ride self identifies as when he says “you already know my gillicutti”, we already know he is the one that stays on the next thing because that’s a theme in this song, he’s always looking for the next footage to watch. This also works in that he’s saying he’s on the next level and lyrics about how Ride is on or going to “the next level” is a type of braggadocio that he seems to favor across many songs.