In this case, the hardware limit is CPU time. NES Tetris will give you more points for clearing lines the higher the level is. For example, on level 0 clearing one line gives you 40 points but on level 9 clearing one line gives you 400 points. This is implemented in the code by adding the base number of points to the score in a loop where the counter is the level number: https://github.com/CelestialAmber/TetrisNESDisasm/blob/2bd89... NES Tetris is written with the assumption that its main game code won't run for more than one frame. When the player reaches a high enough level the "add score for cleared lines" code will take too long, and the processor will get interrupted for the start of the next frame while it's still adding the score. This causes the game to crash.
The Tony Hawk's Pro Skater games can crash this way. If you cheat and enable perfect balance, then you can grind infinitely on a circular rail and eventually the score is so high it crashes the game.
That’s what I think makes the Tetris feat so incredible. There’s no cheating needed. This is being done on the base game after something like 40 years.