As per your other thread this will probably need to be custom-built Looking for a Plugin that counts Taxonomies
Looking briefly at the site in your screenshot - it may appear visually like what you are after but it does not look like it is dynamically populating the information (if it is then it is doing it via a custom built feature), which is a long way from what you describe above
That said what you are after (if just using a list of different categories with quantity of posts) shouldn’t be that hard to build - although you will need the site setup to understand different properties and agents as posts.