The Crop Factor vs. Increased Magnification Problem

I encountered a problem when listening to TheSnapChick:
https://www.youtube.com/watch?v=UJQOmvX9fgs
at 1:46 min.
where she (approximately) said that "if you take a photo of this guy with full format camera he looks like this (him in whole figure) but when you change the camera to a Nikon D500 (DX type) he'll look like this (image showing the upper body of guy, apparently closer up).

Fantastic! I thought.
Just minutes later I checked at Scandinavian Photo:
https://www.scandinavianphoto.se/nikon/af-s-nikkor-200-500mm-f56e-ed-vr-1020842
selling this lens and one of their selling arguments was "corresponds to 750mm at a DX-type camera".

Aha, I thought TheSnapCick was right!

But, but, but... Problem: Does it really work like that??

Well, it doesn't!
This is what's happening:
The upper image corresponds to a full frame camera, the lower to the DX-type camera
Moving the lens to the DX the field view angle get smaller and as a result, only part of the guy to the left can be seen in the smaller chip. Looking at this image,camera in hand, it looks like the magnification has increased.
It hasn't!

The upper part from photographyelement.com and the lower the same, modified by me!

I'd say both TheSnapCick and Scandinavian Photo (depending on what they mean with 'corresponds to') were wrong. (UPDATE 2020-09-14  Not! There seems to be a knowledge gap between a group of knowledgeable users and those not so knowledgeable. The former seems to know the difference between those two cases and feel it's OK to use an expression like "corresponds to 750mm at a DX-type camera" (I don't agree), some of the latter think the lesser view angle means magnification. I've got clarifying answers from both Scandinavian Photo and TheSnapChick on this subject.)

If one looks at the image of chip sizes it's like this:
The image data in the red square (Nikon D500 (DX type) is exactly the same as (in the same area) in the full frame (blue square), no smaller, no bigger.  This will be the case independently of the pixel density of the smaller chip, the field view angle stays the same (smaller) and that's what creates this apparent increase in magnification when presented on a screen in full-screen mode

Lastly: I enjoy TheSnapChick's YouTube videos enough to enlist on her courses, I need to learn more about photography and she knows a lot.

UPDATE:

The best complete lesson of the interplay between the different factors to take into consideration when it comes to decide how lenses work (and eventually which to choose) is this one:

https://www.youtube.com/watch?v=f5zN6NVx-hY

When trying to understand complexities, it can help to watch problems described in more than one way. Tony Northrup has made another one concerning the same subjects:

https://www.youtube.com/watch?v=DtDotqLx6nA

These guys have done a range of useful Youtube videos, it's worth wile to check them out!