Here's a better ChessBase link:
https://en.chessbase.com/post/charlie-storey-interview-2020 By the way, this isn't Storey's first DVD on The White Sniper. He also did one in 2011 for Foxy Video, #134.
"The Sniper" (black) isn't an independent opening, and Storey doesn't even maintain a consistent approach to it. I don't remember exactly where, but Storey said that he has played various setups after 1...g6, 2...Bg7. Actually that makes sense. It's one of the advantages of the Modern Defense, black still has some choices about how to play the center pawns.
"The White Sniper" also isn't an independent opening. If black sets up the classical center with 1.g3 e5 2.Bg2 d5 then white will get to snipe at it. But if not, then white, being white, will have to make some commitment first, and the usual result will be a transposition to some other opening. I agree it would be helpful to know if that means the English on this ChessBase DVD.
The "Sniper" name is pure marketing aimed at Storey's junior students. In a way it's annoying, but since I'm old and not so idealistic anymore, I find it easy to ignore. As for the opening itself, both 1...g6 for black and 1.g3 for white are valid ways to begin. Storey knows a lot about these openings, enough to inspire Henley to do a four DVDs series for Foxy Video in 2011. (Actually seven DVDs if you count his earlier three on 1.d4 g6 2.c4 Bg7 3.Nc3 c5 4.d5 Bxc3+.) I fast-forwarded through these videos just to know what was on them, in case I wanted to really watch them later. What stuck in my mind was the number of times Henley said "sniper".