I believe that as a society, we have to stop saying that raspberry pis are powerful without adding “…considering their size and price” 
I agree that there is a great potential, and the specs are reasonable on the high end model (compared to, say, an mid range android phone from 2015). But if I read another article saying “the new raspberry pi is closer to a desktop machine than ever before”, well… let’s just keep it relative.
Those 3 requirements should be solvable, but if not, and/or you want a small x86_64 device, you could get one of those compute sticks with Celeron CPUs, or one of those mini PCs inside a tiny cube.
They’re slightly bigger than a RasPi and I’m not sure if you can replace their Win10 installation.
Well first I am going to try and get and Android app working on the pi (I think getting the app to boot at start up will be the most complicated part, but I am going to try Emteria, whose free tier product includes a “kiosk mode”). So that really is a useful tip. If that doesn’t work, I will get a celeron mini-pc and either use it with windows or, if possible, linux.
update:
OK! I have installed Lineage OS and managed to get my app running!! I formally retract my previous statements about the power of Raspberry Pi.
I have one huge challenge remaining: I can’t get my gamepad (generic USB gamepad, a PlayerX PCB from pimoroni) to work. I am investigating now, any help would be greatly appreciated.
Update 2:
I have now got most of the buttons working on the pi with lineage on gamepadtester.com. I can rewire the buttons to get all of the buttons I need, but I still need to get the input into defold. I’ll check how android works with gamepads as I haven’t read the manual on this yet.
Update 3:
Project complete!
I ditched the playerX and i am now using a reprogrammed makey makey, which works like a normal keyboard, so the pi picks it up no problem. It also has arrow keys and a space bar, so it’s possible to navigate the UI and open the app, meaning that I don’t need to autorun it on boot. Performance is absolutely perfect (the pi gets nice and hot, too, which I assume is a good sign, right?). Doing it like this- with no hacks, legitimate Android app on a legitimate Android installation on an arm chip - is incredibly satisfying.
@masterneme, without your suggestion, I would never have considered an android installation. Thank you so much for that.
No problem, I’m happy to help.
If the Pi gets too hot it will throttle hard so you may want to take care of that.
I might try underclocking, but first I want to check the temperature and see if it’s actually significant or not. 50° feels hot but isn’t actually too bad.