Tableau Server already provides this facility. A user will only be able to see Projects they have the rights to see and 'on click' of the Project (which you can display in thumbnail or list view) they will be presented with only the Workbooks they have access to. The security is all built into Tableau Server. You can set the 'Projects' page to be the default starting page for any user hitting the server. Trying to recreate all this functionality including the security in a separate portal is probably do-able but I'd seriously question the requirement as it'll require long-term commitment to maintain & adapt to any changes to the security model Tableau introduces with later versions of Server.
Projects actually don't show user content as thumbnails UNLESS the user/admin him or herself modifies details of the project in question. There is no supported way to "automatically" download the user-provided images in this case.
You can use the REST API to generate and download a thumbnail of any user-created view on the server. You can read about the REST API here:
The specific method you want is called "Query View Preview Image".
That said, the image that YOU pasted into your question is not user-created. It represents built-in analytics by Tableau Server showing how many times a specific view has been executed by users. This particular image cannot be retrieved via the REST API.