Yes,
as far as I am aware, the game would not run on Windows RT. For that reason you would need the Surface Pro as the Pro version of the tablets run the full version of Windows 8. (I have the Surface Pro 2, presumably my thoughts also apply to the original Surface Pro.)
In answer to your question I had a few problems initially with the game (inadvertent firing of smoke, apparently unable to enter some hexes), but they all ceased once I disabled the trackpad tap-to-click-mouse feature (and instead just use the trackpad buttons). For that reason I have concluded accidental clicking was the source of my problems. It's been a few weeks now without any problems at all.
I'm also regularly playing one turn on my desktop, the next turn on my tablet when I'm on the train or whatever, without any issues.
(Wider thoughts: I have to say the Surface Pro had exceeded my expectations - it's a little heavier than an iPad, and more so with the keypad cover (essential for JTCS and other serious work

), but unlike the iPad it's a proper computer with a proper OS.)