Third-polarizing-filter experiment demystified – how it works

The key is that a polarizing filter can deconstruct the light into its components. A vertically polarized filter doesn't ONLY let through light that is exactly vertically polarized, but it will pass through the vertical component of all the light, and block the component orthogonal to the filter.

So the three filter setup is rotating the polarization at each step (while also decreasing its brightness) and as long as two consecutive filters aren't at 90 degrees to each other you can keep going with as many filters as you want.