Include files in child themes, declare in functions.php

When it comes to the template hierarchy, WordPress will indeed look in the child theme directory before loading from the main theme.

For all other non-specific WordPress files (like functions and 3rd party includes), it’s entirely up to the main theme to decide how to load them.

Unless the theme is using locate_template to load these includes, or is checking the stylesheet (child theme) directory first, your file overrides in the child theme will have no effect.

If the functions are wrapped in if ( ! function_exists( ..., then the author has allowed for overriding, and you can simply write your own version of the function in your child theme’s functions.php.

Failing that, look for any do_action( ... ) or apply_filters( ... ) around the code you want to alter – this is your last port of call for overriding default behaviour in your child theme (check out the codex on hooks).

If none of the above has been implemented by the original author, you have one of two options – edit the original theme, or contact the author and make a request to implement an API for child themes.