Movable Frame Tetris
Instead of moving the falling brick, move the entire tetris frame in the rain of tetris parts; make the frame walls semi-permeable sometimes, and emulate life and medical interventions.
This would be a simple modification of tetris game to emulate functioning of an organism (the tetris frame) moving around and eating blocks of food (raining tetris blocks), and medical interventions (varying permeability of the walls) to help relieve clogging, as described in the ShapeFlow idea.
So, imagine a rain of liberally-spaced tetris blocks and a free-floating rectangular frame on the screen. The brick translation (left-right) controls would be turned off, and user would position the bricks by (left/right) controlling the location of the entire tetris frame instead. The brick rotation controls would remain as in normal tetris game, but would affect only the brick that is within the horizontal range (the box shadow in x-axis, "longitude") of the box, so, to rotate a brick, you'd slide the entire tetris frame like the horizontal paddle in Atari Breakout), but the "paddle" in this case is entire tetris frame, and use the rotation controls when a particular block is in x-range.
To emulate the medical interventions to fix the organism, the left-right side-walls would get temporary permeability when "eating" a "medical" brick, or using a collected points to call this "medical help". The permeability could be visualized as blinking or dashed-line left-right walls (or fragments of walls), and work by allowing the user to insert the falling bricks from the sides to complete a row.
Properties of the permeable walls would be varied -- from a wall that allows to inject tetris bricks from the side to complete a row within, to the walls that allow tetris bricks to slide out (like flowing water) from the frame through a hole in the side wall, emulating some different medical clearing procedures to help metabolism. The special modes of the walls, could bring-in other fun features, like changing of brick chirality (handedness through mirror image of the brick) upon the brick entering the frame (as described here), and other magic features.
The purpose of such tetris could be to explore the intervention space, allowing to survive the ever-faster rain of tetris blocks, to explore the survival curve distribution to improve human longevity.