Something I discovered while researching this post: Sega had their own Super FX-y thing with the Sega Virtua Processor. It was only used in one game (https://en.wikipedia.org/wiki/Virtua_Racing), but the thing I find most fascinating about it is that Sega contemplated releasing just the Virtua Processor itself—you guessed it, as a lock-on cartridge.
(Unfortunately, this fact didn't really fit in anywhere, so I'm just dropping it here.)
There was a hobbyist who developed a port of Wolfenstein 3D to the Game Boy Color that worked the aame way: the cartridge embedded an ARM processor that actually ran the game and copied the graphics into the GBC's tile memory for display.
It looks most like what the parent said, the sort of DSPs in the late 80s and early 90s used as GPUs.
NES carts actually have an audio pass-through that can replace/remix the built-in APU sound. Atari 2600 does not, but the DPC gave it three-voice music. How? The CPU has to read from the DPC once per scanline, then manually shove that value into the volume register, generating the audio waveform at a 15.7 kHz sample rate.
This... sounds strictly worse than the modern game download. If I have an SNES and everyone has moved to making cartridges with included GPUs, then to play three new games I have to buy three games and three GPUs.
If I have a computer and everyone has moved to making games that require a new GPU, then to play three games I need to buy three games and one GPU.
That hardware cost inefficiency is a big reason cartridges lost to discs. (and, later, downloads)
Interestingly, modern GPUs are also sold bundled with the games that run best on them!
https://www.amd.com/en/gaming/raise-the-game https://www.geforce.com/whats-new/articles/destiny-2-geforce...
Yet we're still expected to pay the same prices we were paying back then - even more in some cases.
My favorite example is Star Fox for Super Nintendo, a cartridge that came with a GPU, allowing 3D graphics. https://en.wikipedia.org/wiki/Super_FX This was in 1993, five years before GPUs became mainstream on PCs.