Can you tell me if what you are trying to install specifically identifies itself as a beta? Does it actually say beta?
The one I am downloading now does not say beta on it. However, going to the store page - it still identifies as Early Access.
In my download list, all it has is the icon of the game - downloading 7.2gb and just says Divinity: Original Sin.
The Beta did not identify itself as such in the Steam interface in any way. I suspect that it what you're downloading, as the full game will not likely be available until after Steam's daily roll-over at 10AM PST
Also, even though my Larian Vault account has been updated graphically as those above have stated, the keys have not. They are still the same Beta access keys even though they are not identified as such
