I think that video gives you the best idea with regard to game streaming, looks like it works just fine. I've never done that kind of thing as my main pc is an HTPC so why use 10/12" when I have 40" available
As to tablet use, the S3 will work just fine. I've both the Sp3 and S3, and while the experience is better on the SP3 due to the extra power and the ssd, the S3 is the right form factor. The SP3 works fine as a tablet, and I had no issues using it as such, and then I got the S3 and realised just how much nicer the surface is at 10" (other than the limited kickstand!). It really is the sweet spot for tablets imo, especially with this aspect ratio. But froim my experience, the SP3 is utter overkill as a tablet, and I think that you will also find that a tablet with a fan is quite annoying at times! (game on the SP3 and your fan will more often than not be funning at full tilt, which is very audible (not necessarily loud, but it emits a noise that you can't easily ignore, unlike a typical computer fan which just blends into the background (I guess it's also the proximity of the fan to your ear))
In terms of comparing it to other tablets such as android etc, well I've mixed experiences. I went from a nexus 10 to a surface 3, and my take is this: The S3 is both faster and slower than the Nexus 10. Some tasks are quicker, some are slower. However while it is often comparable in performance to the nexus 10, things are just a lot easier to do on the S3 because it is a fully fledged feature full OS, not an OS dumbed down so 5 year olds can pick it up and go, and it's often the case that it just takes longer to accomplish a certain thing (just as a very basic example, organising folders and files (pics and videos etc) is so simple on a windows machine regardless of the type of input, wheras on android it's largely a long winded slow PITA.
Personally (with that video making my mind up with regards to game streaming) my opinion is that you'll be very happy with the S3. My only complaint about the s3 as a tablet is the kickstand. It may work for some, but for me and the way I sit and lie etc, the angles just aren't the ones that offer me an optimum viewing angle. the SP3 spoilt me.
Tablets should be fanless!
