You can click on the name of the third-party seller in the "sold by" section to the right below "buy now" to get user feedback and some more info about them. Doing so shows that the seller only has 43 lifetime reviews, with only 15 in the last year, 33% of which were negative. Some of the user feedback comments include...
"Beware! I was unable to activate the Windows because the product key was already used on another device!"
"I did receive the email with the new product key but the key still does not work. My pc is now unboorable. Requesting refund"
"USB didn’t work but cd key did so was able to get it done."
"This item is supposed to be the full retail version of windows 10 pro. After installing it identifies as OEM, not retail! Also, the usb stick is corrupt and would not install. I had to create and use an install usb drive from the windows site to get install completed. I need a new Full retail license key that I paid for provided."
"OEM key not valid, will not allow registration with Microsoft"
"This is not a valid microsoft key."
The only items this seller has for sale appear to be Windows 10 keys and "Silicone Stretch Lids (Surpise)". From the looks of their feedback page, they get overwhelmingly negative feedback from the keys, while the lids appear to be there simply to keep their feedback rating up high enough to avoid getting kicked out by Amazon.
So no, I would not expect these to be valid retail copies of Windows 10 Pro. If I had to guess, they're probably grey-market keys intended for sale in other countries that they got for next to nothing and bundled with some Windows 10 USB drives that they also got for very little without keys, and then packaged up nice to look like something resembling a new retail copy. If you want to buy Windows 10 from either Amazon or Newegg, either OEM or retail, you should make sure that it's being both shipped and sold directly by those companies and not through a third-party seller. Otherwise you might as well just be taking a chance with a much less expensive grey-market key.
Also, if you are looking to save money, Windows 10 Home will be nearly identical to Pro for the vast majority of people who don't require the handful of additional mostly business-oriented features that pro includes. See here for the differences to determine whether your wife would actually even need those features...
https://www.microsoft.com/en-us/windows/compare-windows-10-home-vs-pro
You can, for example, get a retail copy of Windows 10 Home on a USB drive "sold and shipped by Newegg" for the same price. Or a download copy without the USB drive for $10 less. Or a non-transferable OEM copy for even less.