Even though it has been suggested that it might just be that the restaurant is for discerning customers only, I thought that this site's behavior was very bizarre. I figured that no restaurant would want to exclude any potential customers, even if it only excluded those still using IE11, which admittedly might not be a bad decision.
In my mind, this was a fault in the programming of the site. So unless the "missing" cipher suites, that Win 10 supports, are added to Win 7 and Win 8.1, this problem will continue to occur, because lazy site programmers will continue to exist, and will probably grow in number. Of course, those of us who never use IE if at all possible, and instead use a legitimate browser, might never run into the issue, but I think it is still worth knowing about. And I think it would be a good thing if all of the TLS and PSK cipher suites that Win 10 supports could be added to Win 7 and Win 8.1, if possible. TLS Cipher Suites in Windows 7 shows how to select the order of the cipher suites that are used by IE and your OS:
...but I believe that is only applicable to the cipher suites that are already a part of the OS, and to add any that aren't probably requires an update, like what was done with this one - https://support.microsoft.com/en-us/help/3161639. I have no idea whether it is possible to add the ones from Win 10 somehow, officially or un-officially, but it would be nice. Of course, if site programmers would just stick with Steve Gibson's cipher suite suggestions - https://www.grc.com/miscfiles/SChannel_Cipher_Suites.txt - that would also solve the problem.
I also thank @VistaLover for his testing and reporting his findings. Very informative.
Cheers and Regards