Please note, that you can run analytics reports at one of 4 different scopes: Farm, Web Application, Site Collection, and Site. The Farm/Web Application scoped data is available via Central Administration. The Site Collection/Site scoped data is available within each Site Collection/Site.
Based on the url you have shared, it appears that you are trying to get at a Web Application's "Top Pages" report (via Central Administration).
The bad news is that this data is not available through any APIs, nor is it stored in a database where it is supported to be queried directly. The best you could do is export this to a Spreadsheet (using the Analyze tab in the Ribbon). After it's in the Spreadsheet you have a few options, none of which are fully automated:
- Upload it to a content area and access the data in it via Excel Services APIs.
- Import the data into a (SQL) database that you own and can write your own queries against.
Use a tool like Fiddler to see if you can get at the Web Request being generated to Export the spreadsheet. This may help in getting it more automated.
Remember, by default, the data in this report is updated nightly, so you whatever you come up with your users will be looking at day old data, so you don't need something pulling "live" data.
If you are curious about this, and want to see where the data is coming from, you can do some detective work to track this down. For example, turn on SQL Profiler and trace the queries. It should be pulling from the Web Analytics Reporting (not Staging) DB. Please note, however, that it is not supported to read from the Web Analytics database. Doing so can cause harm to your farm and leave you in an unsupported state. It is only supported to directly query the Usage and Health Data Collection database in SharePoint: