How to write from my overwolf app to the local file system?

Is OW includes any built-in API for writing files?

First, you need to ask yourself why you want to write to files.
Have you considered to use the localStorage API or cookies?
Anyway, for very simple writes you can use the overwolf.io, but it’s not efficient and you will not have the user’s PATH variables.
If you want to write to files it’s better to use our simple IO plugin.