That's a technique used/required by some software cracking methods - override your general network DNS lookup process (I believe anything you put in the "hosts" file in Linux/Mac, and the similar file in Windows - though obviously don't quote me on this - will be used rather than DNS-queried). So you configure say "google.com" to go directly to 127.0.0.1 (the localhost address, pointing right back at your own computer) and run a server on the port that the program is expecting to authenticate to.
The problem is responding to those API requests in a way that the program will accept - if it's just a simple PING, no issue, but if there's any sort of more advanced encryption, handshaking or license checking/exchange going on, you'll need to reverse engineer the algorithm. Some simple versions of that you can just record once and "replay", but most will at least have a timestamp hashed in.
(super rough, lay-man's understanding of the issue - sorry for any inaccuracies)