I would argue that TGM is closer in spirit to NES Tetris than to modern Tetris. In both NES and TGM, the speed of the game is extrinsic - it comes from the game itself, forcing you to play faster and faster.
In modern Tetris, the speed is intrinsic - it comes from the player skill. Even with forced 20G the rotation system and the wall/floorkicks mechanism makes it much more easier to both move and recover from screwups.