Well, his whole thing is over engineered. He doesn't need a PIR sensor (the LEDs can just be on all the time), he doesn't need RGB addressable LEDs (he can just connect an LED to a GPIO port with a resistor). He also doesn't need a computer with the power to handle a web server.

So, what you need is a machine that has WiFi connectivity plus GPIO plus a few components. I'd suggest that you can do this with a Raspberry Pi plus a small WiFi adapter.

Using Amazon.co.uk pricing:

  Raspberry Pi Model B:       £42.89
  Raspberry Pi Power Supply:   £3.95
  Edimax WiFi Adapter:         £8.15
  Some LEDs + resistors (est.) £2.00
  ----------------------------------
                              £56.99

Which is $90. Of course, if you have any of these things (like an old USB WiFi adapter) you can cut the cost further. Or you can do as I do (see link above) and reuse old equipment. My bus monitoring project was done for the cost of the LED display from SparkFun ($12.95).

And the Pi has a lot of power to do other stuff. I have other ambient stuff in my house running off a single Raspberry Pi plus it's doing CCTV motion detection as well.