Custom post type not rendered into frontside nav menus

Do I need to write a custom nav menu walker to encompass my custom post type objects ?

A snap of the Themes > Menus page: https://imgur.com/e3KuVTi

Here’s the entire plugin as it currently stands.

defined( 'ABSPATH' ) OR exit;

register_activation_hook( __FILE__, array('Fixtures','activation_handler'));
register_deactivation_hook( __FILE__, array('Fixtures','deactivation_handler')); 

add_action('plugins_loaded',array('Fixtures','init'));

class Fixtures {
	protected static $instance;
	public static function init() {
		is_null( self::$instance ) AND self::$instance = new self;
                return self::$instance;
	}

	public function __construct() {
		$this->plugin_url = plugins_url().'/fixtures';
		if( is_admin() ) {
			add_action( 'init', array( $this,'create_post_type'));
		}
	}

	public static function activation_handler() {
		global $wp_roles;
		$wp_roles->add_cap('administrator', 'manage_fixtures');
		flush_rewrite_rules();
	}

	public static function deactivation_handler() {
		global $wp_roles;
		$wp_roles->remove_cap('administrator', 'manage_fixtures');
		flush_rewrite_rules();
	}

	function create_post_type() {
		error_log(__FUNCTION__ );
		$labels = array(
		    'name' => 'Fixtures',
		    'singular_name' => 'Fixture',
		    'add_new' => 'Add New',
		    'all_items' => 'All Fixtures',
		    'add_new_item' => 'Add New Fixture',
		    'edit_item' => 'Edit Fixture',
		    'new_item' => 'New Fixture',
		    'view_item' => 'View Fixture',
		    'search_items' => 'Search Fixtures',
		    'not_found' =>  'No Fixtures found',
		    'not_found_in_trash' => 'No Fixtures found in trash',
		    'parent_item_colon' => 'Parent Fixture:',
		    'menu_name' => 'Fixtures'
		);
		$args = array(
			'labels' => $labels,
			'description' => "Custom page post-type which restricts title edit & post delete",
			'public' => true,
			'exclude_from_search' => false,
			'publicly_queryable' => true,
			'show_ui' => true,
			'show_in_nav_menus' => true,
			'show_in_menu' => true,
			'show_in_admin_bar' => true,
			'menu_position' => 15,
			'menu_icon' => '/wp-content/plugins/fixtures/img/padlock.png',
			'capability_type' => 'page',
			'hierarchical' => true,
			'supports' => array('title','editor','page-attributes'),
			'has_archive' => true,
			'rewrite' => array('slug' => 'fixture'),
			'query_var' => true,
			'can_export' => true
		);
		register_post_type('fixture',$args);
	}
}

Removing the
if( is_admin() ) {
condition from around the add_action('init',...
did the trick.