Custom output format for maps?

I would like to create a custom exporter to output to my game engine’s format. Is this possible with scripts? Any simple examples/tutorials?

Yes, as of Tiled 1.3 this is possible using JavaScript. Python may also still be an option for you but it is harder to set up. Please see the documentation about scripting, and in particular this small example outputting a custom JSON format:

Binary formats are also supported, by using the BinaryFile class.