The difference between a library (like CGI.pm) and a framework (like Mojolicious) is that you call library functions, but a framework calls your functions. That's called "inversion of control".
If you write a CGI script, you do things like checking the URL, and if it fits certain criteria, you do stuff. If you write a web application with Mojolicious, you tell that it shall call a certain function when a certain URL is fetched.
The idea is that this saves you from repetitive tasks like checking URLs, parameters, HTTP method (GET, POST, ...) etc.
Basically, is it right for what I am doing?
Probably. Follow the examples from Mojolicious::Lite, it should be quite simple.