App Store app missing from first gen. apple TV

To elaborate on the above. The 4th gen and 4K are the only models that run apps. If you have a 2nd or 3rd gen (black box with silver remote) then they have preset content sent via server.

If you are only seeing the computers and settings icons then you are not properly connected to the network

Make sure DNS is set to auto (settings - general - network)

If on wifi try ethernet

Test on another network

The 1. Appletv looked like this https://www.01net.com/tests/apple-apple-tv-1g-fiche-technique-2421.html

it never had or supported an App Store of any kind, nor did the 2g or 3g only the 4g and the newest 4K model do

if the 2 later dont have access to the internet it they will only display settings and few other things.