I was faced with the task of setting 7-Zip file associations across a domain.
This looked like an appealing solution until I found it doesn't work with 7-Zip, because the 7-Zip installer doesn't register with the standard Default Programs handler.
I updated your WiX file as a result. (Your sources are quite helpful!)
Defining Installer Components states to include a file and registry entries that refer to it in the same component, so I did some of that, too.
Along the way, I enabled advertisements to work, and Add/Remove Programs now shows your icon.
Since you had set ALLUSERS=2, it looked like you were about to implement Single Package Authoring, so I implemented that.
Unfortunately, upgrading a previous per-machine install requires passing ALLUSERS=1, eg,
msiexec /i 7z1604-x64.msi ALLUSERS=1
to force the installer into per-machine scope before upgrade evaluation: the FindRelatedProducts Action has already run before the UI could switch install scope from per-user (recommended default) to per-machine.
Hopefully, someone more gifted at this than I can find a good solution.
This is a start, however.
The files intended to update yours are 7zip\7zip*.wx[si].
The solution as provided builds with WiX Toolset 3.11 and its Visual Studio Extension.
Correction: The files intended to update yours are
7zip\7zip\*.wx[si]
in the attachment.