If it looks like a duck and it walks like a duck, why is it not a duck? If you are using a DSP to process graphics, then at least in the context of your system it has become your graphics processor.
Plenty of GPUs don't have (or aren't used for their) display output. It's a GPU because of what it does: graphics processing. Not because of what connectivity it has.
It does do graphics. Calculating graphics is different from handling display output. You can separate the two.
Like someone else mentioned, laptops often have discrete graphics cards that are not wired to display hardware at all, needing to shuffle framebuffers through the onboard graphics when something needs to make its way to a screen.
> Like someone else mentioned, laptops often have discrete graphics cards that are not wired to display hardware at all, needing to shuffle framebuffers through the onboard graphics when something needs to make its way to a screen.
Those are GPUs even if they aren't connected to a display because they still have graphics components like ROPs, TMUs and whatnot.
You're free to define it that way, but that's substantially different from GP's "if it's not a display adapter, it's not a GPU" that I was pushing against. It does seem pretty fragile to define a GPU in terms of the particular architecture of the day, though. There's plenty of things called GPUs that don't/didn't have TMUs, for example.
Plenty of GPUs don't have (or aren't used for their) display output. It's a GPU because of what it does: graphics processing. Not because of what connectivity it has.