The application is not yet publicly available, but it's not difficult to guess that it uses a local web server. "It's heavily leveraging another project that I've been working on for the better part of 2 years," says the author. The project is probably AndroidAsync.
Here's a demo:
I'm sure we'll see Koushik's app or a similar app in the Google Play Store pretty soon. It will make Chromecast more useful. The next step would be to mirror the device, but that's a lot more complicated.
Right now, Chromecast is only available in the US, at least officially. If you're not in the US, you can try eBay and buy one for $45-70 + shipping fees.
Speaking of Chromecast, it's interesting to know that it doesn't run Chrome OS. It's based on the Android TV code. "It's actually a modified Google TV release, but with all of the Bionic / Dalvik stripped out and replaced with a single binary for Chromecast. Since the Marvell DE3005 SOC running this is a single core variant of the 88DE3100, most of the Google TV code was reused. So, although it's not going to let you install an APK or anything, its origins: the bootloader, kernel, init scripts, binaries, are all from the Google TV."