Is it somehow possible to purchase or otherwise activate a game that has been removed from the Steam Store?
You can use a third party to buy a key from and then activate it on steam. Please keep in mind during the purchase wherever you find the game you are looking for key make sure it can be activated on steam!
The answer of woof is correct, but there is another way. The original 'The Elder Scrolls V: Skyrim' can't be found anymore by searching if you search in steam. If you search for Skyrim, you get the newer version. You can still visit the page through your browser though if you know the link.
However, someone who has the original game still in their library can still navigate to the store page and buy the game as a gift (I tested untill I had to purchase).