I think it's a simpler design, and it's more ergonomic to swipe horizontally with your thumb than vertically. It was also likely designed with that Siri Remote in mind, which means you can swipe faster to scroll faster.
And it might bother some people enough to buy more stuff... like a brand new iPhone or Apple Keyboard!
Well, Apple had a new way of navigating in tvOS with the swiping of the Siri Remote. The style of on-screen keyboard reflects this new way of navigating.
I personally find that both navigating with the Siri Remote and entering stuff on the on-screen keyboard is very tedious.
There was also the Siri feature to enter in info, but this was very problematic. In tvOS 9, Siri didn't work that well. Also, not everyone wants to announce a password to their accounts to everyone around them.
But probably the biggest reason for Apple to have the style keyboard that they do is that there is no D-pad on the Siri Remote which is ideal for the square style on-screen keyboard. In later versions of iOS, Apple added the pseudo-D-pad by touching the edges of touch pad, but their on-screen keyboard never changed to the more ideal style.
My guess is that Apple won't change it any time soon.
I almost never use the on screen keyboard why would you? using your phone with the apple is much faster and easier for me and I always have it on me. Good for keyboard stuff or just use Siri. even with the appletv remote why don't you just use Siri? but for real the Apple TV app on iPhones is awesome. you don't really have to look at your phone after you get used to it and its much better for a remote than the appletv remote.