Elegance is the world's first Lightroom Web Engine to be distrubuted as a Lightroom plugin. Not only does this greatly simplifies the installation procedure, but the greater flexibility provided to plugins also allows Elegance to automatically check for updates each time Lightroom is restarted. Behind the scenes the plugin handles the installation of the Web Engine for you.
Unzip the download. You should now have a web engine called 'Elegance.lrplugin'.
The plugin is installed via the Lightroom plugin manager.
If you have donated towards the project you should unlock the trial version using the registration code that you should have received.
Important note for Windows users of the original distribution
If you're a Windows user and you have installed the original Web Engine then you'll need to delete this manually. If you had followed the original installation instructions then you can find it here:
where LightroomRoot is the location of your Lightroom installation (probably inside C:\Program Files\Adobe\).