At PhotonsToPhotos charts in the section labeled DxOMark Derived use data from DxOMark.
Currently the 5th section on the main page.

But the majority of the charts and data at PhotonsToPhotos are not from DxOMark.
This includes all the charts in the 1st section on the main page.

More details to follow but the PhotonsToPhotos noise floor is a function of the Circle of Confusion and so it does take image size (and viewing distance) into consideration.

More details in a later post but 12-bit versus 14-bit at ISO 6400 with that camera would not have different dynamic range and would not show any differences in the deep shadows.

Not the upper limit for something like Photographic Dynamic Range (PDR) unless you mean more smaller photosites at the same sensor size.
PDR will go up when you are able to collect more light per unit area in the final image as opposed to per unit area on the sensor.

Definitely yes for a measure like Photographic Dynamic Range (PDR).
Think of it this way, noise becomes acceptable when the signal rises far enough to mask the noise. That signal carries photon noise with it, even if it's a small amount. You can see this on the Photon Transfer Curves (PTCs) at PhotonsToPhotos. See the attached example. The black dot marks PDR. Read noise alone would be about 2 stop to the left.

The distinction I was making earlier is that DxOMark Landscape DR is based solely on read noise whereas PhotonsToPhotos PDR uses a Signal to Noise Ratio (SNR) where noise is all forms of noise not just read noise (for example photon (shot) noise).

It would have been better if your sentence had ended here.

Because your not understanding is why you come to a wrong conclusion.
It is the perfect comparison if you are a photographer who is ultimately creating an 8 x 10 image and you want to compare how different sensors will perform.
There are other measures at PhotonsToPhotos that are at the pixel level independent of sensor size.

FWIW, the original post clearly refers to the Photographic Dynamic Range (PDR) measure at PhotonsToPhotos.
PDR is documented there so your ignorance seems willful (to me).

Respectfully,

Screen is pixel level read noise and that is what I call Engineering Dynamic Range (EDR). Print is simply the Screen value "normalized" for pixel size. Screen has nothing to do with DX versus FX. DxOMark has no information for crop modes; period.DxOMark publishes nothing that is relevant for crop modes; period. Any correlation you see is coincidental.Well, actually, I do predict that for cropping DX from FX, and it is helpful to know when comparing.

Roughly but not strictly proportional to the area used.

The low ISO settings are important and there the difference is as I stated.
For example at ISO 64 11.63 for FX and 10.90 for DX is a difference of 0.73

The original post:

The quick answer:
Since you mention PhotonsToPhotos to are talking about Photographic Dynamic Range (PDR).
PDR is measured using a standard final image size and viewing distance (not unlike Depth of Field (DOF))
PDR also uses a Signal to Noise Ratio (SNR) criteria (unlike DxOMark which uses only read noise).
Since the DX image has to be enlarged more than the FX image the SNR is lower resulting in a lower PDR.
Pixel size does not matter.
Also, remember, we're talking about the capability of the sensor and not some specific image of a scene with a particular dynamic range (the horsepower of your car is the same travelling at 10 mph than it is at 55 mph you're just using less of it).

For a measure like PhotonsToPhotos Photographic Dynamic Range (PDR) (and even DxOMark Landscape Score) pixel size is largely irrelevant; what matters is pixel performance per unit area.
The differences between sensors come down to differences in how cleanly the pixel data is read out (read noise) as well as differences in something called Full Well Capacity (FWC).

At PhotonsToPhotos but not at DxOMark.

Not true. At DxOMark their dynamic range is based entirely on something called (pixel) read noise and "normalized" for pixel size (resolution).
The SNR 18% charts have nothing to do with their dynamic range.

Except that it's not in proportion to the crop factor.

That is only a rough approximation. The details as to why not are in the article I cited earlier:
DX Crop Mode Photographic Dynamic Range
For example, for the Nikon D850 the drop in Photographic Dynamic Range (PDR) from FX to DX is about 3/4 stops while your reasoning would imply something closer to 7/6 stops.

Substantially correct.
Not to derail things but we need to be clear about how apparent noise is as opposed to how much noise there is.
The larger sensor has more noise and more signal than the smaller one; but noise is less apparent because it has a higher Signal to Noise Ratio (SNR).