GAME only hold 4.4% of the UK retail market for videogames now. You're also just looking at the website which frequently runs out of stock of products.
Just Dance 4, Wonderful 101, Wii Party U, Assassin's Creed 4, Lego City Undercover etc are also all sold out online. Along with a large number of Vita games (inc most Vita hardware bundles).
I think low stock rather than mega sales is the reason.
I can't comment too much on GAME's website and how it runs. Being Australian, I have little experience with it. Perhaps you're right on that front. Or perhaps Wii U gamers are tending to go to GAME moreso than other gamers. I honestly cannot comment to any significant degree on it.
What I can say is that JB HiFi in Australia typically keep quite a decent amount of stock, tend to be one of the more preferred retailers with regards to gaming, and are sold out of it in almost all stores. I suppose I'm somewhat extrapolating from that result in suggesting other explanations.