I don't think this quite works. It seems like the simple strategy is to carve off a fully contained 1x2 "room" on the bottom row for the red dot, play normal Tetris except make sure you never clear the 2nd lowest row, and then just every now and then move the red dot back and forward in the room.
That trivializes one of the two simultaneous games you're playing, and then what's the point? (You might be tempted to say "just don't do that, then", but players will gravitate to the optimal way of playing, not matter how boring.)
My feeling is that you probably need some kind of separate scoring system for the dot-moving game rather than have it be just a binary end game condition and that scoring system needs to reward either variability or risk.
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Dodge the falling blocks and complete lines to survive!
Tetris [Move with ←/→, rotate with ↑, soft drop with ↓, hard drop with space]
Player [Move left/right with A/D, jump with W]
Staying in the same spot for over 10 seconds results in game over
That trivializes one of the two simultaneous games you're playing, and then what's the point? (You might be tempted to say "just don't do that, then", but players will gravitate to the optimal way of playing, not matter how boring.)
My feeling is that you probably need some kind of separate scoring system for the dot-moving game rather than have it be just a binary end game condition and that scoring system needs to reward either variability or risk.