How to get "Apps usage activity" report via Google report api
"Apps usage activity" is under Admin console\reports
You can follow first this documentation to know how to set up your application's authorization. The Authorize Requests documentation shows you how to set up your client's authorization using the OAuth 2.0 protocol. The request must be authorized by an authenticated user who has access to that data when your application requests private data.
You can also check these SO question and tutorial about Google Analytics Core Reporting API with C#. It allows you to query report data. Each query requires a view (profile) ID, a start and end date, and at least one metric. You may also supply additional query parameters such as dimensions, filters, and segments to refine your query.