(I may be remembering older tech) A baseline answer is that film records light at the surface of the emulsion and spreads it downwards through the gelatin, while sensors are a bunch of toilet paper tubes with lenses at the top that only collect light at the bottom of the tube. The farther away from the central axis the more obliquely light from "standard" lenses hits the sides of the tubes instead of going all the way down.
"Modern" lenses are designed to shoot light down the back end straighter than film designs but the effect is unavoidable. Note that even on film you'll get vignetting but not as severely, and that several extreme wide angle lenses have graduated ND filters to counter the vignetting... Even high end Red cameras exhibit this effect, as seen here in their literature:
http://www.red.com/learn/red-101/lens-vignetting
Physics is a harsh Goddess and demands much from her followers.