I know the terminology has gotten quite loose in recent years with Nvidia & Co. selling server-only variants of their graphics architectures as GPUs, but the "graphics" part of GPU designs make up a significant part of the complexity, to this day.
That's not a good definition, since a CPU or a DSP would count as a GPU. Both have been used for such purpose in the past.
> There's still use for GPUs even if they're not outputting anything.
The issue is not their existence, it about calling them GPUs when they have no graphics functionality.
Edit: perhaps your point is that it doesn't make sense to call a device designed primarily to accelerate ML workloads or just general purpose vector calculations. In that case I'd agree that GPU isn't the right name.
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.
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.
The "G" in GPU doesn't imply that they have to render directly to a screen. In fact, professional graphics cards are commonly used for bulk rendering for animating videos.
Datacenter GPUs are mostly used for AI these days, but they can nevertheless do graphics work very well, and if they are used for generative AI or if their built-in super sampling capability is used, the distinction becomes rather blurry.
On the other hand, they also left out some features that you'd expect to find on a general-purpose compute accelerator.
For example, they focus on tensor math. No support for bit wrangling and other integer math. No exotic floating point formats. Minimal branching capabilities.