Is there any script so I can show the option to export all of my plugin's tables in this default wordpress tool?
The Core export function only outputs data from the
prefix_postmeta tables, so it would take a lot of doing to extend it to export other tables entirely, especially since it converts everything to XML.
Instead of trying to modify this core function, it would be much simpler if your plugin's data could be saved in those tables by using custom post types instead of custom tables. As you can see in your screen shot the custom post type "Movies" automatically appears here. This would be more futureproof than extending core functionality.