Accessible and translatable Genesis reponsive menu

accessible-genesis-menu.php

<?php


/**
 * Enqueue javascript for responsive menus
 * 
 * Pass localized strings to the javascript. Replace "prefix-" with your 
 * child theme prefix and "textdomain" with your theme textdomain. The strings
 * will be available for translation in your pot-file like normal
 * 
 * @uses wp_enqueue_script
 * @uses wp_localize_script
 */
function prefix_enqueue_scripts() {
	
	// create an array containing the data you want to access in your js
	$prefix_javascript_options = array( 
		'screenReaderNavHeading'     => _x( 'Main navigation', 'Screen reader navigation heading', 'textdomain' ),
		'responsiveMenubuttonText'   => _x( 'Menu', 'Responsive menu button text', 'textdomain')
	);

	// enqueue the script
	wp_enqueue_script( 'prefix-responsive-menu', get_stylesheet_directory_uri() . '/js/responsive-menu.js', array( 'jquery' ), 1.0.0, true );
	
	// pass the data to the script - script handle, js object name, php data 
	wp_localize_script( 'prefix-responsive-menu', 'menuData', $prefix_javascript_options );
}
add_action( 'wp_enqueue_scripts', 'prefix_enqueue_scripts' );

responsive-menu.js

jQuery(function( $ ){

	// by using wp_localize_script, we now have a menuData object we can use to get all localized strings

	$("header .genesis-nav-menu, .nav-primary .genesis-nav-menu").addClass("responsive-menu").before('<h2 class="screen-reader-text" id="rian-main-nav">menuData.screenReaderNavHeading</h2><button class="responsive-menu-icon" aria-controls="menu-primary-navigation" aria-expanded="false">menuData.responsiveMenubuttonText</button>');

	$(".responsive-menu-icon").click(function(){
		var _this = $( this );
		_this.attr( 'aria-expanded', _this.attr( 'aria-expanded' ) === 'false' ? 'true' : 'false' );
		$(this).next("header .genesis-nav-menu, .nav-primary .genesis-nav-menu").slideToggle();
	});

	$(window).resize(function(){
		if(window.innerWidth > 768) {
			$("header .genesis-nav-menu, .nav-primary .genesis-nav-menu, nav .sub-menu").removeAttr("style");
			$(".responsive-menu > .menu-item").removeClass("menu-open");
		}
	});

	$(".responsive-menu > .menu-item").click(function(event){
		if (event.target !== this)
		return;
			$(this).find(".sub-menu:first").slideToggle(function() {
			$(this).parent().toggleClass("menu-open");
		});
	});

});

This is a translatable version of https://gist.github.com/RRWD/e248ca84ef680c5341f1

I have tested your code.
I have the following suggestions. I am not very good at coding, but would my best to explain.

1. In accessible-genesis-menu.php, line 23, for the "1.0.0", the two full-stop are in different colors (one is blue and one is red), which suggest that the syntax is wrong. This can be fixed by enclosing 1.0.0 with ' ' .

// enqueue the script
wp_enqueue_script( 'prefix-responsive-menu', get_stylesheet_directory_uri() . '/js/responsive-menu.js', array( 'jquery' ), '1.0.0', true );

2. In accessible-genesis-menu.php, line 18 and 19, please add a comma after line 19, that is
   'responsiveMenubuttonText' => _x( 'Menu', 'Responsive menu button text', 'textdomain'),
   Also, someone may use __( ) instead of _x( ) for translating string.
   That is

'screenReaderNavHeading'     => __( 'Main navigation', 'textdomain' ),
'responsiveMenubuttonText'   => __( 'Menu', 'textdomain'),

3. In responsive-menu.js, line 5, the translatable variables menuData.screenReaderNavHeading and menuData.responsiveMenubuttonText are in the ' ' string, and this makes the translation fail to work.
   You should change it to something like ' + menuData.screenReaderNavHeading + ' and ' + menuData.responsiveMenubuttonText + '
   which close the previous string, add variable and then open the next string.
   That is to change line 5 to something like the following:
   $("header .genesis-nav-menu, .nav-primary .genesis-nav-menu").addClass("responsive-menu").before('<h2 class="screen-reader-text" id="rian-main-nav">' + menuData.screenReaderNavHeading + '</h2><button class="responsive-menu-icon" aria-controls="menu-primary-navigation" aria-expanded="false">' + menuData.responsiveMenubuttonText + '</button>');

Thank you.