Its kinda hard to see how this layer of air is going to transfer heat when air is better off an insulator than a conductor.
You are incorrect sir.
For those who don't understand, here's a crash course in physics.
There are three total ways for heat to be transferred; radiation, convection, and conduction. Examples of these are:
Radiation: The sun has a functionally empty void between it and the Earth, yet it transfers energy to us through radiation.
Convection: Think ovens. The heat comes from the element, but the entire fluid (air inside the oven) gets hot. Hotter fluids and cooler fluids mix and flow so that they come to thermal equilibrium.
Conduction: Normal heatsinks. Direct contact transfers thermal energy from one body to another, through the contact surface.
Now, fluids retain heat at different rates. Think about it as such, the air temperature can vary several degrees during the day. In the Midwest of the US it has been recorded to be sunny and warm (~70F) during the day, but drop down to below freezing over night. On the other hand, Lake Superior never changes mean temperature by more than a few degrees over the course of a week. This illustrates that the thermal capacity of water is different than that of air.
Moving on, the temperature of something is determined to be either stable, cooling or heating. This is determined by the flow of heat. Imagine that you have a bucket, which has holes along the side. You begin pouring water into the bucket. The bucket is an object, the water being poured in is heat being generated from operation, and the holes are transfer of heat. You heat up if the rate of water being poured in is higher than the rate it drains from the holes. If you pour water in at the same rate it is being drained you've got a constant temperature. If you pour water in slower than it drains you've got cooling.
Combining these three ideas, we can discern the following:
1) Air needs flow faster over a heatsink (as compared to water or oil), in order to have the same heat transfer rate as those fluids do (combine lesson 2 and 3).
2) Air contact can be just as effective as other fluid contact, given the right conditions. You can increase convective cooling dramatically, and make it as effective as conductive cooling (combine lesson 1 and 2).
So, as far as hydrodynamics goes, I'm going to glaze over most of that, given it would take a semester in college to get anything besides the basic idea. Be forewarned.
All known fluids (yes, we theorize perfect fluids exist, but can't replicate them on Earth) have a viscosity. Viscosity is the tendency for a fluid to resist flowing. Think honey (viscous), versus water (less viscous), for an example.
Viscosity is a property of both the fluid, and the forces applied on the fluids. Think about swimming in water, versus hitting it at 80 Mph. So the faster you move, the greater the viscosity of a fluid. Air is a fluid, so at some speed the viscosity of air will actually be a palpable force.
Combining this, a flow of air moving at great speeds could act like a solid, and provide enough force to separate two other solids.
This is the idea behind an air bearing. A device moves so fast that the airflow it generates creates a "cushion" for the component to ride on. As the friction from fluid shear is significantly lower than that of kinetic friction (solid moving across another solid), you get a low friction bearing that has an ideally limitless lifespan due to not being worn away.
Now combine hydrodynamics and thermodynamics, and you get this fan. Fast airflow creates a cushion for the fan blades to ride on (functionally 0 noise, due to 0 physical contact). Fast airflow allows both efficient convective and conductive cooling to occur. The only problem that remains is the motor driving the fans. A brushless DC motor could generate a long lifespan, low noise, extremely efficient cooler. If you were to use a noisy motor, you can account for the noise in the video. Everything else is legitimate, but there are two remaining concerns. Construction to the tolerances required may be an interesting proposition, and the quickly spinning fan blades are a major concern. If Sandia can finally overcome that (i.e. why these aren't already in production) then they've got a winner.
Edit:
Thanks Kreij, I did screw up the name. It has been changed to read conduction properly. Whoops.
Edit:
Arrgh, another error because typing being faster than my brain (yes, intentional screw-up there). Thanks to Completely Bonkers for finding my capacity/conductivity screw-up.