Change github diff to be side by side comparison?
Seems it has been moved. (At least when reviewing PR files)
Yes, it is possible since Sept. 3rd 2014: see "Introducing split diffs":
Diffs now come in two flavors, unified and split.
Switch between them on pull request, commit, and compare pages using the toggle in the top right of the page. The mode you last used will become your preferred default.
Note: since Sept. 4th 2014, it also support word diff highlights.
See "Does Github have a view that shows diffs between file versions?".
Since 2014, and the introduction of dark theme(!) in 2020, the UI is now:
- from Unified:
- To split diff:
using: 
Note: adding "&diff=split" at the end of the URL will give you the same result: a split diff.
Not git diff, but you can use git difftool, which will call appropriate utility for your platform to do just what you are asking for.
For example, in Linux it will call meld by default, which is very nice tool. git difftool knows about quite a few diffing utilities, but you can also configure it to call your own.
You can with Octosplit Chrome extension. But you don't get the full length.