On the specifics, I'm afraid nobody can for now. They have refused to peer-review their protocols and validation data, so their assays are essentially a black box. So far, incredibly, they have managed to get away with this thanks to a glaring regulatory loophole (as the article explains); but sooner or later they'll have to open up if they want their assays to be taken seriously by the medical community.
In broader terms, however, there's been a lot of recent work in the well-established microfluidics [1] literature on whole-blood assays [2], so that can give you a good guess about how they go about their implementation: most likely some form of "lab-on-a-disk" centrifugation for plasma separation and subsequent transport to separate microfluidic optical chambers preloaded with colorimetric reagents for readout, using perhaps a digital camera and some non-kosher/black-boxy form of curve-fitting DSP to increase "sensitivity".
In all I'm very skeptical until they open up and provide peer-reviewed validation data for their assays. There are already several companies doing patented blood microfluidics like Abaxis [3] with peer-reviewed validation, and the enabling technologies have been out in the open in the literature for years, if not decades; so the whole "we are doing a super duper secret awesome thing we can't tell you anything about" sounds rather D-Wavey and fishy to me.
[1] http://en.wikipedia.org/wiki/Microfluidics