OK - I misunderstood slightly, but I think the idea is the same. I thought you were intending to write a project in the Arduino IDE based upon the linked project. You could do that and use your Arduino as ISP.
If you just want to implement their project then I think you should be able to use their existing .hex file and simply upload it using AVRdude, using your Arduino as an ISP programmer. I think recent versions of AVRdude are set up for that without any fiddling but I have never tried it so you may need to await a more seasoned Arduino ISP user! My understanding is that you would upload Arduino ISP to your arduino board, connect the CS, MISO, MOSI and Clk pins of the two chips then tell AVRdude to upload to the ATTiny using Arduino ISP as the programmer.
I don't think it will be difficult with a little guidance but unfortunately I don't quite have the right experience to lead you any further on this one. Keep at it thou' - I'm pretty sure this can be done.
Ugi