The projector is straight up DIY projector construction. The difference is that DIY projectors usually actually use decent resolution screens (I myself built one, back in the day when I had little money and lots of time) and are also much larger. This stuff made sense back when 1080p projectors were hideously expensive and you could get a cheap laptop 1920x1200 LCD screen, strip off the backlight, and build an oversized but functional projector out of it for much less.
The design certainly works, but it's highly suboptimal as far as light loss. The color filters in the LCD mean that you only get 33% of light output; after the polarizer, that's down to 15% or so. That's why they need noisy fans and yet they're very dim. And yes, their lamp is bog-standard HID crap, not an actual projector bulb. They even have the rear reflector that looks identical to the one that I used with my DIY projector. The one good thing these projectors have going for them is that the replacement bulbs are dirt cheap.
This is the 1024x768 one that I built back in 2007. Same construction: standard HID light bulb, reflector behind, fresnel lens, panel with backlight stripped, fresnel lens, output triplet lens (sorry, I don't have a photo of the innards). At least mine had an e-ballast instead of the crappy magnetic ones, and seems like it was brighter too!
I actually spent some money rebuilding it as 1920x1200, kind of gave up on it since it wasn't that bright and kind of loud, shortly thereafter got a real job, and bought myself an Epson EH-TW3200 instead.
You should take apart a real projector sometime; it's a world of difference :-). Yes, the construction inside this cheapo scam projector is "decent" once you start with the premise that you're going to build this kind of projector, but the design has nothing to do with the way real projectors are designed. Real consumer projectors either use a DLP chip and a color wheel, or dichroic color splitters and 3 high-density, monochrome LCD panels arranged around another dichro prism. The light path is also much narrower and much tighter in real projectors, none of this wide-open crap with wiring next to the lenses!