You discuss Carmack's pixel scrolling and miss the fact that this guy here who claims he did "the same" just had to draw one character of the snake's head at the new position, overwriting the previous head with the "body" character. And the tail character with the "empty" character unless the snake eats something.

What in the world has that to do with Carmack's algorithm of updating Mario after one pixel hardware scroll (after which he has to redraw the "unmoving" part fully) and adding more background once he spends the hardware moves?