The thinking here is probably along the lines of having an X% chance to die every gate, eg 10%. Then the 'difficulty' or likelihood of surviving is 0.9^n with n as the score etc. It's not really accurate, but you can get where the 'multiplied exponentially' is coming from.

That said, the game is actually about luck the better you are at it - if you are skilled enough to always get through the gap if your bird starts near the gap, then the difficulty comes down to chance - how far away the gaps are vertically from each other at each step.