And considering how much work we've done to cut down on latency, I wouldn't expect the Steam streaming app running over a generic VPN connection to even come close in performance -- the VPN is almost certainly going to run over TCP, while AppStream will run over UDP, meaning in any but the best network environments AppStream will clobber a VPN connection for latency.
[1] https://aws.amazon.com/appstream/
[2] Disclaimer: I work on AppStream for Amazon, but my opinions are my own and don't represent Amazon. I'm just commenting as someone who has a lot of experience playing with the product.