Actually - the game itself is not trying to run as administrator.
The game is trying to get some libraries installed which it requires, and this requires administrator access. Once the libraries are installed, the game will run in user mode without elevated privileges.
If you read the popup, it should be clear that it's the Steam client requesting the privileges, as it is this that is trying to install the libraries that Civilization VI needs.
Now, one reason why you may need to do this more than once is because the game is fresh out, and there were probably a small number of minor day one updates coming out in quick succession. Any change to a library requirement can cause the request for elevated privileges. (Personally, I've been asked this only twice, out of at least a dozen starts of the game from Steam over the weekend).
However - there are reports of other games getting stuck continually asking for the VC Redistribution package to be updated on startup.
This seems to be some kind of client data cache issue with Steam.