You are not mistaken.

In the early days of the PC, there were lot’s of GPU options, as in literally dozens. So the first part of the question is why did they almost all disappear? The answer to that is that it became a much more complicated market with Windows, with way higher demands on the software side, and many hardware vendors suck at making software. So over time the best combo of hardware and driver beat out other high end manufacturers so we ended up with just 2, and the on-board / on-chip GPU made every low end 3rd party GPU next to irrelevant, with very little possibility of making a profit.

The low end chips were no-longer needed, as they can now be had cheaper and more efficiently as part of the CPU for both AMD and Intel. And since these are the only 2 CPU options for X86, Now that VIA has discontinued their X86 line acquired from Cyrix, there is no low end entry point in the PC market for a new maker of GPU.
The natural evolution is to start from a lower end, and if successful work up. This is not possible in the PC market, and makes entry to the market near impossible, except with enormous investments that may never pay off, especially since PC is a dwindling market.

As you mention Intel is dipping their toes, but despite doing a pretty good and big effort, and investing a lot to develop a better GPU, and actually delivering a good product at a reasonable price, that should be absolutely competitive on paper, their marketshare is absolutely minuscule, because Nvidia and AMD together dominate and already fill the needs for the mid to higher end market, and have brand recognition for graphics.

It’s not that there aren’t technologies that possibly could compete if scaled for PC, because those are actually pretty numerous on phones and tablets. But you can’t port these cheaply to PC, because there is no market segment for them to slide in to easily.
It would require major investments to make them actually hardware performance competitive at higher scales, and investments in making good drivers. Intel had a big head start in these aspects, already making on-chip graphics that had drivers already. And still they are struggling, despite delivering a good product, and people have been screaming for a third option,because of high GPU prices.

This may not be the entire explanation, but I think it’s a very significant part of it.
The better question IMO is why Intel never became more popular, considering how much people have raved that more competition in the GPU market is required.

And the explanation for that is:

but let’s be real, AMD and nVidia are the only options

Except Intel actually presented a good alternative, but was never seriously considered by most people for whatever reason.

Personally I didn’t consider Intel, because I remember earlier attempts by Intel, where Intel quickly left the market again. And I didn’t want a GPU where I’m left without driver support a year after I purchased it.
So in my case it was lack of trust in Intel to stay the course. But every other maker would have that exact same issue.
There have been a few attempts in the past from other makers, but they all had performance or driver issues or both, and left the market quickly . Intel delivered a stellar product by comparison. And if Intel drops out of GPU again, I think there’s a pretty big risk it may be our last chance for a third significant mid-high end GPU maker on PC.

TLDR:

1. All the old competitors couldn’t cut it on either the hardware or software side, and so they died out.
2. It’s an insanely expensive market to enter and to stay in, with high risk of never making a profit.