Right, I have done it. Sort of. It's one of those things which is simultaneously quite easy and really, really hard.
My first attempt ended as Minnie described, in a complete dog's breakfast of nothingness, like a blind person who had never learnt how to knit trying to do it with two different colours. Not great.
Then I noticed in the instructions that this was a Zimmerman stitch, so Googling took me to this page (and actually the basic brioche rib stitch is quite well described in Her Zimmerness' Knitting Without Tears). Anyway, said page then took me to an entire website about the brioche stitch which began the clarification process for me. The k2togs of the original pattern are here described as 'brk1' or 'brp1', in other words, knit the brioche stitch (regular stitch with the yarn over) as one stitch. A slightly subtle difference in description that helps to clarify what you should and shouldn't attempt to knit together in any given row. Just blindly doing k2tog won't help if you're on the wrong stitch in the pattern.
So, I started off just with how to knit a plain brioche stitch (the first section on this page) and this little sample. Well worth trying to get your head round the concept of the brioche, which is basically to create a standard rib but with a lovely raised effect to make each rib stand out. Not sure the photo does it justice but there are fairly deep valleys between each rib, much more so than you would see by just knitting and purling.
Basically all you're doing is slipping a stitch purlwise and yarning over it to create a messy-looking stitch/yarn over (pics below), followed by knitting or purling together the same messy-looking stitch+yarn over created on the row below. Simples 
The two colour version is basically the same only you do each side twice so that on one side it's main colour rib + contrast colour valley and on the other contrast colour rib + main colour valley. I managed to bugger this up again even on a sample of like 10 stitches but you can see the end I've managed to do right at least. This side is donkey-colour rib with camel-coloured valleys, and this side is camel ribs over donkey valleys.
Hopefully in this example and this you can see that every other stitch looks normal and the one in between is the stitch + yarn over.
The original pattern tries to add a couple of edge stitches to stabilise the edge for a scarf. For the squares I'm tempted to put a couple of bog standard garter stitches in to make it easier to see what's going on, although based on the end that hasn't gone wrong, it looks okay. One of the trickier bits is doing a yarn over right at the end of a row and then making sure it's still there when you come back to knit the stitch again later, the second pattern explains this better.
Marvellous. It does look lovely when you do it right, but godawful when you do it wrong (with no obvious means of recovery).