Gamestream with the Nvidia Shield Portable is the primary reason why I purchased this device.
Gamestream works with Geforce Experience 2.1.3 while using the stock Geforce Drivers (338.xx) that are installed on the Alpha. OR - you can install the custom 344.75 drivers, which will allow the latest Geforce Experience 2.1.4 software to run on the Alpha.
https://www.dropbox.com/s/7l4jiapvvcpr1o5/Win8.1Win8Win7_x64_HDA%28344.75%29.exe?dl=0
^These custom drivers come straight from the Software Manager who developed the Alienware UI that is used on the Alienware Alpha. This is NOT my link, and I take no credit for this.
I use Gamestream to play mostly Dark Souls, and I have also completed both Wolfenstein: The New Order campaign timeplines using Gamestream. I have never come across a game which wasn't able to Gamestream to the Nvidia Shield Portable using the Alpha.
You can set up a Wifi Direct-Connection to the Nvidia Shield Portable using the Alpha's internal Wifi dual-band antenna while bypassing the router. You can initiate Wifi Direct-Connection on the shield. You only need to do this once, and then after that - the Alpha will automatically recognize the Shield when it's turned on. I've tested this and it works just fine.
However, I choose to let a wireless router to mediate the data between the devices. This allows Gamestream to be used Remotely while the device is on a different network (like when I'm traveling). I'm using a DLink 860L dualband router rated at AC1200. Using the 5 Ghz channel allows the Shield to Gamestream games with video quality at 1080p at 60 FPS. While using the 2.4 Ghz channel, only 720p is available at either 30 FPS or 60 FPS.
The Alpha has no problems Gamestream-ing at 1080p when using the 5 Ghz channel. There is very little latency. Compared to Nintendo Wii U's Off-TV Play, Gamestream-ing with the Alpha and Shield is just a very VERY TINY bit delayed. Compared to PS4 and PS Vita, called Remote Play, the response is much quicker on the Alpha + Shield. So overall, I'd rate the Gamestreaming capabilities between the Nintendo Wii U + Gamepad and the PS4 + PS Vita.
A 3rd-party open-android app which uses Gamestream, called Limelight, shows only a 3 millisecond latency on average using the 5 Ghz channel, and 11 milleseconds using the 2.4 Ghz channel. The average latency is actually calculated by the Limelight app itself when you exit Gamestream.
Nintendo Wii U Off-TV Play > Alienware Alpha + Shield >>>>> Sony PS4 + PS Vita Remote Play.
So yea, I've tried Gamestreaming on the Shield using the Alpha.
EDIT: Woah, the link to custom 344.75 drivers are now expired. I don't mind upping a link to the drivers if anyone asks at a later time. I'm currently not logged onto the Alpha because I'm "studying for finals".