vimeo on apple tv

If you wanted to verify you can always go into the settings - general - about, to see the model number. If it were a 3rd gen then those only have preset channels that are sent via server. In looking at their site it appears that they no longer support older models of Apple TV, and instead require the app that runs on the Apple TV HD (4th gen) and 4K (5th gen)

The 3rd gen never ran apps, but rather relied on specific channels that used basic templates and were sent to the device using a server. That model is now well over 8 years old, so it doesn't exactly fall in line with that statement. The fact that Apple still went ahead to develop a server version of their TV app and support it via subsequent firmware updates says a lot about their commitment to legacy devices. However, it would also be up to the other providers to continue to dedicate their resources to a device of that vintage and most are not willing to do that. Vimeo is hardly the first, and as time goes on many more are deciding to drop it (most recently YouTube and CBS announced they are ceasing support).

What model Apple TV?

Identify your Apple TV model - Apple Support