@iainfarrell: I really, really like this idea and would definitely like to be involved if it comes to fruition. Please register my interest and keep me posted. If Hyper Light Drifter is confirmed as the first game then I'll pick it up ready for next month.
Also, if you're into the concept of a "video game book club" then I feel obliged to recommend Giant Bomb moderator @thatpinguino's own podcast project, Deep Listens. Every two weeks, he and his co-hosts play the same game and then dive deep on its gameplay, story and presentation, bringing their own backgrounds in literature and philosophy into the discussions. I admittedly only listen to the episodes pertaining to games which I've already played, as it's become a bit of a tall order for me to get through a game every two weeks (one a month sounds way more manageable for me), but it's nonetheless one of my favourite video game podcasts out there. Plus, they were kind enough to have me on as a guest for an episode on Oddworld: Stranger's Wrath a few years back.