On the demo, the button doesn't appear for 5 seconds.
From the main menu, after playing the game and dying and clicking the 'x' in the top left to quit, the game goes to the nag screen. It's the same screen that appears when you start the game, with with an icon in the bottom left to click if you want to buy the game and one in the bottom right to continue to the menu - only the bottom right icon is missing. After about 5 or 6 seconds the button that lets you end the game appears - the button says something like 'Fight evil another day' - and the game finally lets you click it and leave.
When I get home, I might fire up a screen capturer and upload a video to demonstrate the behavior for you.
Since you don't believe me, you can see what I mean at the tail end of http://www.youtube.com/watch?v=n8YKYKgqzSs
(And despite this now interminable forum conversation, it's certainly very far from being the worst crime against gaming out there. Grumbling about it has already eaten up more than it's fair share of time and effort on my part!)
And that button is clearly labelled 'Buy Now!'. I don't know which school of user interface design you went to, but when I see a link labelled 'Buy Now!', I figure that if I've no intention of buying the product, then I've no business clicking that link. I don't think I'm an atypical user in this regard.
Plus, since clicking that link does bring up your online store in a web browser (which, I'll reiterate, I've no intention of using), no matter which way you cut it, it still counts as an obnoxious nag and a user interface peeve.
What's more, it's not immediately obvious, in these days of in-app purchases and whatnot, that a link marked 'buy' will exit the game. For instance, suppose this demo was downloaded from a Steam account with some actual cash attached (I don't know if your demo is on Steam, this is a hypothetical), there's no way that I, as an ignorant user, can tell whether you've made some arrangement with Valve or if there's some call in the Steam API where clicking the app can extract the money from my account to automatically buy this game. Similar things are already in place in mobile app stores.
Asking users to go clicking on your 'Buy my product' links willy-nilly is definitely much worse than the behaviour I was originally grumbling about!