I think it's an interesting idea that gives a true sense of starting each day afresh.
Here's a reminder of how it all works:
The Today page uses a custom page template and is set as the default home page of the blog. This runs a custom query to check if there any posts from today and list them in chronological order - if not it says so.
The Today page also does a bunch of other things such as "On this day" and on-the-fly building of the Daily RSS feed each time it loads. The full content of this is also loaded into the database ready for the Daily Email to be created overnight.
I have then customised the normal WordPress archive template for when the view
is_day() to replicate the look and feel of the Today page, keeping things consistent between days.
In the footer I dynamically create the previous/next day links (inserting yesterday or today accordingly) based on the dates involved. These links then open the archive page in the day view.
There's not really that much too it, it's just a different approach to the standard reverse-chron default that younger with WordPress.