Child themes let you override templates, but these are not templates you’re attempting to override. You can’t drop in arbitrary files and override the parent theme, and WordPress can’t do it’s magic when include or require are used to load files.
The reason this works for templates, is because WordPress doesn’t load them with include, instead it uses filterable functions with custom logic, such as get_template_part.
So there is no way to use the child theme method to swap out that file.
You do have the advantage that the child themes functions.php loads first.
Instead, you’re going to have to look at how the code in that theme loads itself, if it provides filters and actions, etc, much like you would when trying to override plugin code.
You’ll need to contact the vendor for documentation and support, afterall you’re a paying customer.