Indeed, Borders did go under, maybe Waterstones will too once their primary clientèle get old and die. But in that case then every high street shop is doomed for the same reason.
The point I'm trying to make is that high street shops fundamentally cannot compete with online stores on prices. Can't be done. Simple economics will keep online overheads significantly lower than high street ones and that gap, however narrowed, will never be overcome. As such, there is no point in GAME or any other high street store trying to make price their primary battleground. Their prices should be as low as possible obviously, but it's a battle they can't win. Instead, what GAME should concentrate on is what they can offer that the online shops cannot; namely a hands on, interactive, service-driven environment. Play pods, comfy sofas, maybe a drink or something while you try out a game. Hell, have a system where you can pay £5 for an hour's free playing and if you like it, they'll take the £5 off the price of the game.
Would that save them? Don't know, maybe it's simply a business serving a demographic who want to buy online and they should sell up and buy out. All I'm saying is that GAME can't compete on price and should stop trying, and should focus on a battle it can win.
Not all shops, perhaps: you might expect those businesses where immediate feedback is important (say, food, to check its freshness, and clothing, to see how it looks on) would survive. For stuff like games and books, where you can be confident that the online version will be identical to what's in the shops, yes, you would expect the migration to the internet to continue.
But to your main point: yes, of course, you must be right about being able to offer something unique, and something service-oriented could be the way forward. It doesn't sound much like the business that GAME has been in until now, though. To my mind it would be better suited as an adjunct to other services, much in the way that free wi-fi has become a reason to go to the local coffee shop and consume hot drinks. If you were Microsoft, say, would you think about doing a tie-in deal with Starbucks for renting some floorspace for XBox 'experience pods'?