You can also construct such a diff yourself by going to something like /compare/<old commit hash>..<new commit hash>, and those hashes can also be tags or branch names, and should even allow relative stuff like HEAD^.
(I haven't checked the URL just now, but I use both often. It's a little annoyingly hidden, but it is there.)
PS: I checked out your demo. I can't see how to diff arbitrary commits, only revisions of a PR.
As for diffing commits, you can switch a review into "review each commit" mode so that it will create one revision per commit. You can make this the default for a repo but it's not in the demo as it's not the most common way to work. The demo does really need updating, though!
If there are extensive changes from a follow-up review it gets its own commit and specific commit message.
GitHub throws up 404 when I do this. Same with simply trying to view the old commit directly using the `.../commit/<hash>` link.