The issue is that when you open the Facebook mobile app, you will not be able to see the apps/buttons/tabs you have installed on your Facebook page. The reason is that Facebook mobile does not allow any third party apps to be shown on mobiles. This does not apply only to GloriaFood, but also to any other applications made for Facebook.
However, we provide a smart link for posting on Facebook. You may use this link over the "Shop Now" call to action on your Facebook page, or to create pinned posts about ordering. This smart link detects the device type and serves the menu in the appropriate format, including mobile.
You can find your smart link along with step by step visual instructions in your admin area, under Publishing → Facebook. You will unlock Facebook Sharing and Shop Now as soon as you publish the app on Facebook.
You can achieve more, even on mobiles, by extensively using the Facebook built-in features.