The Responsive Menu plugin uses the users screen size to determine when to show the Responsive Menu and when to hide your main menu, as such you will need to set the Breakpoint option to something extremely high so as that it is always triggered by any screen size, something like 8000 should be sufficient.
This is explained further in the page titled How Do I Hide The Original Menu? but you basically need to find the class or ID of your original menu containing element and place that in the Original Menu to Hide option above.
This combined with the high Breakpoint value as specified above will mean that only the Responsive Menu is ever showing on your site.
From the FAQ
Why won't my menu show?
License Activation Issues
How do I Build a Menu Like the Responsive Menu Website?