Modern graphics cards are essentially miniature supercomputers in their own right, with their own memory and instruction sets, but in the eighties and late seventies, a very common kind of personal computer design had a single memory bank that was updated by the CPU and read by the video chip, with this being the primary method by which the two communicated.
Were these video chips specific to the CPU they were designed to work with, or could they be used with a different one? For example, could you take the ANTIC from the Atari 800, the VIC-II from the Commodore 64 or the video system from the BBC Micro and put them in a Z80 computer? Could you take the Amiga chipset and put it in a 286 machine?
In most ways, I would expect the video chip to be indifferent to the model of CPU; it really just cares about what data gets written to what memory location. The concern I would have would be the bus protocol, which varied with CPU. For example, the 6502 has a predictable on-off cadence to memory access, which makes it easy for a video chip to access memory on alternate cycles, whereas the Z80 is more complicated. But then, even 6502 computers are not quite so simple in practice, as discussed in the answers to Z80 and video chip contending for random access
So could an existing video chip be used as-is with a different CPU, or would it need small changes (design tweaks, extra/different glue logic, performance compromises like in the Amstrad 464 which simplified the Z80 memory access pattern by rounding every instruction up to 4 cycles), or would it need radical design changes?