For Premiere Elements System Requirements for versions 13 to 8 and the older versions, please see the Adobe Document
Regarding what versions will or will not work on certain operating systems...I would question even your Photoshop Elements FAQ reference.
What Adobe has not tested is not the same the impression that the program does not work on a certain operating system it has designated as " - ".
I have not seen a Premiere Elements document comparable to this FAQ document that you present for Photoshop Elements.
I have found no problem installing and running Premiere Elements 4, 7, 8.0/8.0.1, 9.0/9.0.1, 10, 11, 12/12.1, 13/13.1 on Windows 7 Professional SP1 64 bit or Windows 8.1 64 bit.
The version updates, if available, should be used to give special obvious features as well as other less obvious ones.
In the case of the current version, Premiere Elements 13/13.1, Windows XP, Windows Vista, and OSX 10.7 are not supported. Interestingly, I have found that you can
download the Premiere Elements 13 tryout from Adobe to a Windows XP computer, but you cannot install it.
Also, on a comparative basis, Premiere Elements version 32 versus 64 bit application
Premiere Elements 10, 11, 12, and 13 are 64 bit applications only when they are specifically on Windows 7, 8, or 8.1 64 bit computer.
Premiere Elements earlier then 10 are 32 bit applications whether they are run on Windows 32 bit computer or Windows 64 bit computer.
Premiere Elements 9 was the first version to be offered for Mac as well as Windows.
Premiere Elements Mac was not available as a 64 bit application until version 11 - and with Mac 64 processor.
Premiere Elements as a 32 bit application will block you from importing still images beyond a certain total pixel count.
Lots of other details, but let us start with these.
Please let us know if you need clarification on any of the above.
Thanks your answer was both fast and complete as I need.