A Podcast Of Unnecessary Detail just did an episode talking about the SNES Doom port and how it used LUTs for trigonometry as the SNES didn't have a graphics processor.
It absolutely did! Even the NES had one. In addition to the (cloned) Motorola 65c816 SNES CPU, the PPU (picture processing unit) was a custom chip that offered several different layouts for spitting out tile based backgrounds and sprites as each scanline physically drew across the CRT TV. It was even capable of fancy things like background rotation and scaling (Mode 7, think Mario Kart) and hardware transparences which you can see in many games.
Furthermore, in the case of Doom (and games like Starfox) the cart was baked in with the "Super FX" chip that handled the 3d calculations. So you were actually dealing with two graphics processors for that specific title, heh.
Here's a wonderfully (and painfully) detailed series about the SNES hardware by Retro Game Mechanics Explained:
https://festivalofthespokennerd.com/podcast/series-3-episode...
https://github.com/RandalLinden/DOOM-FX