A series of queries to allow you to export the nav_menu_item post type and related data.

WordPressExportNavMenuItems.sql

SELECT * FROM `wp_posts` WHERE post_type = 'nav_menu_item';
SELECT * FROM `wp_postmeta` WHERE post_id IN (SELECT ID FROM `wp_posts` WHERE post_type = 'nav_menu_item');
SELECT * FROM `wp_term_relationships` WHERE object_id IN(SELECT ID FROM `wp_posts` WHERE post_type = 'nav_menu_item');
SELECT * FROM `wp_term_taxonomy` WHERE term_taxonomy_id IN ( SELECT term_taxonomy_id FROM `wp_term_relationships` WHERE object_id IN(SELECT ID FROM `wp_posts` WHERE post_type = 'nav_menu_item'));
SELECT * FROM `wp_terms` WHERE term_id IN (SELECT term_id FROM `wp_term_taxonomy` WHERE term_taxonomy_id IN ( SELECT term_taxonomy_id FROM `wp_term_relationships` WHERE object_id IN(SELECT ID FROM `wp_posts` WHERE post_type = 'nav_menu_item')));