All light diffracts when it's path is restricted - so you can have diffraction when the light is not normal incidence on the diffraction grating. The reason you are taught the normal-incidence case is that the math is simpler.
Diffracted from "tilted light arrays" ... English is a second language perhaps? The interpretation is reinforced by the reference to the angle of incidence and a perusal of introductory lessons in diffraction. We would say "diffraction gratings" in the same place.
This thread was originally in the "Atomic, Solid State, etc." forum, so my first thought was Bragg diffraction of X-rays from a crystal. But that confused me, because with Bragg diffraction you usually do analyze it with the light coming in at an angle!