Depends entirely what you consider a 'long period'.
I was thinking 5-10 years, for that clock you linked to, no one will care. Will anyone be here? If so they'll probably be the few survivors and they'll not care about what time it is only where's the next meal.
Why does everyone assumes the future is all gloom and doom? We have already been in the planet as Homo Sapiens Sapiens for 200,000 years and as "modern" humans for the last 50,000 years. Your 10 years are a drop in the bucket and in 10,000 years we might not be here, at least not all of us, by then I will hope we conquered space for real