How to count the number of unique views of a node?
It depends how much traffic you site has and how big your server is. If you need to create a view count like this, it will require that you disable page cache making your site slower and demanding more resources from your server, or run expensive queries on every node view.

You could do this with Drupal, but there isn't a module that provides this functionality for you. The statistics module will count all views of the node. To implement this you would need to use either hook_node_view or hook_boot and write to a database the nid of the node being used and a token for the user. If you don't want to count anonymous users, you can use the uid, else you would have to use a combination of uid and session id to try not to count the same anonymous users twice.

A better way if you have a lot of traffic is to use an external tool like Google Analytics and then draw data from there.

Both solutions will require custom code though.