Having randomly spotted a Fandom Secret about it, I went ahead and found out more about it. Basically you play this little girl in her bedroom, and the first thing you do is go to bed.
At which point you wake up in a different version of your bedroom and can now leave, which transports you to a 'terminal' with a set of doors leading to a different nightmare. A couple of them lead to labyrinths, one leads to a dark, rainy forest, and one (which you find inside the middle of another one was simply a black screen dotted with random streetlamps. The walls and floors of these nightmares undulate and change colour, and though there are creatures in some levels, such as glowing worms and clocks with legs, none of them really interact with you. Except the ones that hunt you down and kill you. Thankfully you can wake up at any time, save your progress at your bedside desk and go back in.
As for powerups, there is supposedly a knife, a bicycle and (one I spotted but couldn't get to) a jumper. So far all I have is "Become A Lamp" which, fittingly, turns your head into a lamp which you can switch on and off - at least one level is almost pitch-black without it.
I'm working on finding out more about it (like what to do) but so far there's been a couple of unhelpful websites (well, apart from the one I downloaded it off ^_^) including one which promised me "the yume nikki experiance [sic]". I actually found PORN of this game before I found a proper fandom page of it, and most of that was posting Icons.
So far, despite being one of the more bizarre games i've played, this is actually proving to be quite fun, and rather unsettling to boot. A good deal of my friends are into Touhou "bullet-hell" games - which seem to involve holding down the shoot button and pressing left to right, which can't be too hard - and Visual Novels which, sad to say, i'm reluctant to play due to the horiffic anime that VNs give spawn to. So for now this is my one tentative foray into gaming, and it is paying nicely. Just in time for when I need to get back to schoolwork. Great.