This is a PHP library used to access data across various endpoints on NBA websites. The full documentation can be found at http://nbasense.com/nba-api/. This contains installation instructions, usage examples, and runnable/filterable reporting on all endpoints.
If you are having trouble retrieving requests that access stats.nba.com/stats/, it appears that the NBA has blocked off access to these endpoints on some level; this blocking seems to occur on many cloud hosting providers such as Amazon AWS, Digital Ocean, and Heroku.
In my testing, these endpoints have always worked when developing locally.