There is also the matter of history; if I load the demo page, click that button, and press "back" then I'm on the demo page again.
And of course it'll be in the browser history.
I have to question how practically useful this is. Ctrl+W or middle click on tab isn't that far off. Or open private window and close that, which is a smart thing to do anyway.
Never mind that computers and internet access is ubiquitous enough these days that "using the family computer" for this sort of thing isn't really needed in the first place.
Overall this seems like a IE5-era solution that's pretty outdated and useless today. Perhaps even worse than useless because the implementation is so-so and protection it offers low.
Overall, I'd say telling people to use private windows and teaching then Ctrl+W is probably better.