This article doesn't go at all into the details of why NES Tetris is unwinnable and doomed to fail. Let me plug that gap.
The brick wall limitation comes at level 29, after 290 lines. At that time, the pieces drop so fast that they cannot reach the sides of the well before locking into place. The code rate-limits sideways moves of a piece to about 250 ms intervals, so if the game is running fast enough that the piece reaches bottom in less than a second, it's impossible to translate the piece five columns over to the edge. It's not a human limitation; it's literally impossible to keep playing even going frame-by-frame on an emulator. To go beyond 290 lines (or 293 if the 290th was the first of a Tetris), you'd have to stack up pieces on the sides ahead of time, and the absolute limit is about 310.
Modern Tetris games are very carefully designed to avoid such limitations. Modern Tetris games always allow at least a half second after a piece lands before locking it, allowing further moves and rotations. http://tetris.wikia.com/wiki/Tetris_Guideline
So the game of NES Tetris becomes not how long you can survive, but how many points per line you can score in that fixed duration of 290 lines. If every single line of the 290 was a Tetris, the total would come to about 1,500,000. So to reach the game's score cap of 999,999, about two-thirds of your lines must be achieved as Tetrises.
Gameboy Tetris has no such impassable speed tier. You can play Gameboy Tetris forever and many players have scored 400+ lines and 999,999 there.