On the main zeffy page I linked above it references that one of the intel processors affected was released in 9/13. Yours is i5 and that one is i7, but just saying. I am not aware that there is an official list of affected processors.
The reason this problem occurs is that microsoft added a couple lines of code to wuaueng.dll, the Windows Update Automatic Update ENGlish dll file. Within it, it now checks your cpu type when you run windows update and if it does not like what it sees, it branches to the "Unsupported" message that you are getting. What zeffy's program does is simply bypass that message. Since it is downloadable as as msi file, that means that if you do not like it you can just uninstall it the normal way by doing control panel > programs > uninstall.
If the program fails to fix your problem I am sure zeffy will be interested in your situation, and you can open a New Issue to tell him by going to this page:
Issues · zeffy/wufuc · GitHub
I realize you are probably not a programmer-geek and may be hesitant to use this program. All I can tell you is that it was designed to get around this annoying message and it seems to work. I am not aware of any other solution. You could always go straight to microsoft as well, since your cpu is not supposed to be getting this message, but MS may not be helpful, not sure. You could also just reach out to zeffy and ask him directly about your situation, but surely he is going to ask you to run his program first. If you are really not wanting to take any chances here at all, it sounds like you could just live with the annoying message since you are able to still use windows update.
Assuming you are running 64-bit windows7, the download and install file is here (the filename that ends in "...x64.msi")
Release wufuc v0.7.1.81 · zeffy/wufuc · GitHub