As I understand it, this is not a normal photo sharing system.
The central ReadyNAS photos server does not hold the images.
I think it holds a database of where the images are, and who is allowed to see them.
So that people request access from their server, but it then redirects the image requests to your NAS.
My guess is the Desktop application loads the images into the database on your NAS resizing them for the thumbnail display and the large size, and also communicates with the central server to say where the album is.
Then when you share it, a link is made between the album images (in your database) and the people who they are shared with. Whether that is in you local database/application on the NAS or in the central server, I'm not sure. My guess is that it's in the central server.
If you want a "normal" photo gallery, then you can use a HTML gallery creator (I use Lightroom) and copy the resulting mini-website on to a HTML share on your NAS.
But that requires you to open up your network to the outside world and run the NAS as a HTTP server. If you have a router you can firewall the rest of your network and pass all HTTP requests to your NAS so that the other computers are still protected.
But as I understand the ReadyNAS photos system, it works without that setup and without your PC turned on - just accessing the NAS directly.