WARNING #1: IndieGogo
WARNING #2: InDemand
WARNING #3: Fuzzy pictures of Arduino's, Multimeters and other electronics stuff
WARNING #4: All product photos, videos, completely rendered
WARNING #5: Ridiculously low price
WARNING #6: Time-line
Obviously these are not enough warnings...
The old saying still holds true.... "A Fool And His Money Are Soon Parted".
This clock can be made. It is not out of feasibility, but it will cost way more and take more time than they let on. You are not going to run it on an Arduino. There are already Android apps that do what this clock does, complete with fancy faces and pulling in data from newsfeeds and so on. The challenge here is to package in a projector and also provide the means to interact with the device. For example, you can rig up such a clock using these existing devices:
1. Android tablet with HDMI out, and micro-USB to accept mini-keyboard/trackpad or Bluetooth
2. Pico projector with HDMI in
3. USB keyboard/trackpad to plug in to interact with Android tablet (or bluetooth)
So have your custom app installed on the Android tablet, let you plug in (or connect bluetooth) keyboard/trackpda to configure the tablet... like app basic settings, configure WiFi network/password, etc. Finally, output of Android tablet to the Pico projector and there you have it. Need to just power up both devices. The biggest problem is the optics on the projector to allow such angled projection (keystoning issue). Once you have configured the device, it should just sit there and run your clock app and project with minimal user interaction, but if you want to mess around with the settings you could just turn on your bluetooth keyboard/trackpad.
In fact, if they do use an Android tablet they can even integrate Skype since the tablet will have a camera. They can load on the app and you can Skype-chat with someone and see their face on the wall. Also, you could have it cycle through your photo app and be like a slide-show of family photos. Tons of features available if they simply use an Android tablet.
Surely, if they actually could build such a thing as a prototype they could have already hooked up a rudimentary clock like this. The rest would be figuring out how to put everything in a convenient package, tuck all the power and wiring in there and then refine the software. But otherwise you have yourself an Android tablet hanging on your wall which projects to your wall. Not brain surgery. And with the $289,000+ they have now, they can surely buy themselves an Android tablet, bluetooth keyboard/trackpad and pico projector:
ITEM #1:
http://www.amazon.com/Android-KitKat-Tablet-Cameras-Bluetooth/dp/B00KVVAI3CITEM #2:
http://www.amazon.com/QQ-Tech-Bluetooth-Keyboard-Touchpad-Android/dp/B00BALK9CMITEM #3:
http://www.amazon.com/AAXA-Projector-Minute-Battery-mini-HDMI/dp/B007CWDFP6Now the MINIMUM price for such a thing will have to be at least $600-700. There is just too much in there to sell for even $299 for one. It is totally possible to create this clock, but not for the price and timeline they have stated. I am also sure that someone here on EEVBlog or one of the Maker sites (or Instructables) has already everything they need to create this thing (short of the custom app) and that the work involved will be how to take everything apart and re-package it in a convenient wall-hanging package.
If you strip the LCD display from the Android tablet, cameras, battery, etc... you can shave on some cost. Leave in the WiFi module and speaker, bluetooth, and use HDMI output to the pico projector (or some variant). If you can find a small LED projector and have enough room inside you could stick the guts of the Android tablet into the Pico projector and power it off the same supply. Now all you need is to set up your bluetooth keyboard/mouse somehow. Perhaps leave a mini USB port just in case to get in first... turn on bluetooth and set up the bluetooth keyboard/trackpad, then once configured it should automatically detect it every time you turn the keyboard/trackpad on.
Honestly, at this point I would just start another IndieGogo campaign and just sell an "Android Projector" pre-configured with a bluetooth keyboard/trackpad. Let people use it for whatever they want (presentations, gaming, video conferencing, playing movies, projector clock, etc). Certainly melding the 2 devices into 1 package is nothing new. It has been done already, and for only $450:
http://www.laptopmag.com/reviews/tablets/lenovo-yoga-tablet-2-pro