My opinion, anything labeled "redistributable" is safe to leave as is.
What I would look for is "what was installed at the same time as SQL Server?". In your screenshots, you can see that the redistributable packages have an older install date (by several years in some cases) than SQL Server 2008.
My first step, reproduce the setup in a test environment. Then uninstall all of the stuff containing the text "SQL Server 2008" and don't remove any "redistributable" packages. Then see if things work how you expect. Next, install 2016 and test everything you need to. Once you are confident and comfortable that 2008 was removed and 2016 is working, repeat the process on live.
My advice - never ever do upgrades on live without first doing it in a test/dev/sandbox environment. Also, removal of "redistributable" packages will often lead to errors in other tools, so I tend to leave those alone.
The above is all just my opinion on what you should do.
As with all advice you find on a random internet forum - you shouldn't blindly follow it. Always test on a test server to see if there is negative side effects before making changes to live!
I recommend you NEVER run "random code" you found online on any system you care about UNLESS you understand and can verify the code OR you don't care if the code trashes your system.