Firstly, let me say that people don't usually include videos, but it can be quite helpful. Keep that up.

Alright, so my first guess of what is happening is that, since you are using a mobile device with a touch screen, Steam Link seems to be favoring the touch controls rather than your Gamesir, for the most part.

The reason I say that is because if it was actually working with your Gamesir you wouldn't even see the outlines of the screen controls that can be seen in your video.

Here's my proposition:
> Connect Steam Link to your Host device.
> While you are connected, there's that square with "..." on the upper left corner of your screen. Click that.
A menu will open and on the left side should be a huge panel saying "Touch controls".
> You want to go ahead and click on that, until it says "Deactivated" with a red line on top.
See if that does the trick.

In case this doesn't make it, you could also try this:
> By holding your "options / select button", specifically for you, the one on the left part of the Gamesir, that is black, round and small.
> A small menu on the lower part of your screen should come up.
On the right, lower corner, should be a bunch of options.
> Counting from the left, you should check what the second options is toggled to.
It has two modes. The small caption should say "activate mouse mode".
This way your controls won't be interpreted as mouse controls either.