Both your 660 and 1060 use temporal dithering. All the external GPUs I have tested used temporal dithering, but I have actually tested several 660s and a 1060 so I am as certain I can be that yours are dithering [it gets more complex than that, but I don't want to overburden you].
You might want to try using intel integrated if either of your desktops has that. By default, intel integrated uses spatial dithering only (ie it doesn't move or flicker), and this can be reliably turned off using software available here. Also, avoid using VGA cables whilst experimenting as RF noise will affect the signal and what you see on the monitor.
I would strongly recommend you get your own capture card so you can test these things for yourself. I found that simply relying upon my own experience of pain and discomfort was not sufficient to diagnose things. I once thought that only my 660 did not dither and that all other cards did, as the 660 was generally comfortable and other cards (intel integrated for example) caused immediate pain. I discovered after testing with my capture card that the 660 did dither, and the intel integrated did not. Best explanation I could come up with was that the monitor I using needed dithering to be comfortable, monitors use dithering too, so perhaps the superposition of two dithering algorithms made it work. Now I have since found monitors which are comfortable with intel integrated graphics (and its lack of dithering), and I no longer get random pieces of software giving me eyestrain. With the 660 I found: steam; sharepoint on chrome; office 365; and visual studio 2020, caused pain - all of which I can use fine now.
If you get the black magic card I can talk you through using it, and send you my analysis software. Be wary of buying any capture card marketed to gamers though, these will use compression and screw up the analysis.
As for why Chrome, I really couldn't say. All I can do is re-iterate the testing I have done.
gtx 660 + other external GPUs -> temporal dithering on everything in windows -> temporal dithering on chrome,
Intel integrated -> no temporal dithering on windows-> no temporal dithering on chrome.