A few 80s home video games used this principal. I had a table top version of Donkey Kong (about the size of a coconut) that worked like this. I think they preceded the single-, double- and triple-screened handhelds (e.g., Diamond Hunt). I don't think it was possible to play that Donkey Kong in the dark and I have a faint recollection of chasing sunspots around the house for the best playing conditions.
They used to use them in PDAs. They're called transreflective LCD [1] displays. They're nowhere near as bright as a backlit LCD though, and only look good when you've got a good light source.
I mean, more like light coming from the back through the LCD screen into your eyes, unlike transreflective LCDs.
One needs a white tent pitched behind the laptop screen, and one needs to sit facing the sun. You'd be looking into the space of the tent, which is much like the display in the OP demonstration except the source of light is the sun coming through diffused through the tent fabric (and there are no buildings). The bottom floor could be a mirror.
Interesting idea... I don't think I've ever heard of something like that concept before.
I see two problems, though there may be ways to mitigate them: you're facing the sun, therefore it's effectively in your eyes, and you'd probably lose all semblance of color balancing in the screen.
Not that the second is all that important to most people. I've even gotten used to applications like Flux[1] which change the screen's color over the day, and I find it's usually easier on my eyes. Just sayin'.
You could probably do away with the mirror, and just have a white piece of plastic. It'd be diffused by the fabric anyway, there's no need to have something mirror-like to reflect it accurately. You could possibly use the entire back panel of a laptop screen, and fold it up when not in use (brain-farts while looking at my wife's white Macbook).