Why is my iPad telling me “This app is only available on the App Store for iOS devices.” when trying to update App Store?

As lyssa pointed out, you're trying to open the wrong thing. There is an App Store AND an Apple Store. One is the store you buy apps and update apps from (App Store). The other (Apple Store), let's you purchase merchandise from Apple.

You are not opening the App Store. You are opening the Apple Store App, which can be used while at a physical store.

Look for the white "A" on a blue background. That's the App Store.

~Lyssa

What you have shown is a Safari Screenshot that is just the listing for the App Store app on iTunes. You are not using the App Store App, which is on your iPad directly. The App Store app is pre-installed on every iPad, iPhone and iPod Touch sold.

You can try some of the resets on the phone; These are in Settings>General>Reset.

1) Reset All Settings - clears wifi passwords and a handful of other items; no pictures or apps are deleted

2) Reset Home Screen Layout - takes all apps out of folders; might restore the App Store

3) If the first two don't work and you have your pictures backed up, then do Erase All Content and Settings - this removes everything from the device so you can set it up as new.

~Lyssa

The App Store App does NOT need to be updated. It is controlled by Apple. If you have the App Store App on your iPad and it opens, there is nothing you need to do.

It looks like you're browsing the app store with Safari browser. It tells you to launch App Store (it's an app) to update Apple Store app. Look at your iPad display for an icon that says App Store (see picture below).

Use that to update or install new apps. You can't use Safari browser to update/install apps.

I'd recommend you schedule an appointment at your Apple Store Genius Bar. The App Store can't be deleted. It can only be turned off.

Post a picture of what you're seeing.

From the middle of the iPad screen, swipe down to bring up spotlight search. Type in App Store and see if shows as on your device.

This btw, is what the App Store app looks like:

this is what comes up...