I run World of Warcraft on an i3 all in one..... but I don't know how the Surface OS works. Is that true Windows?
You have the Surface Pro (v3 by now) with normal Windows 8(.1) . Andd the Surface RT & Surface 2, which use Windows RT on an ARM processor. As it is quite limited in functionality and available applications, and never really took off (marketshare is for all practical means non-existent) , I'd steer clear of those.
If its a surface Pro it should run fine but only if you have the space to install it. I really wouldn't recommend buying a 64gb model just for that reason as last I heard it only has 23gb actually free and I think the Wow install is basically about the same it would be to risky and tight to try.