Simpson's insight was that the issue of waste gas is always going to be there. With the world population growing towards 11 billion in the next 20 years, the use of 'alternative energy' sources isn't really going to be enough. That many people need a lot of food, and the corn, palm oil and other sugar-based energy alternatives are not keeping up with demand. The world uses around 85 million barrels of oil a day for energy, manufacturing etc, and it seems like the best idea would be to deal with the efficiency of the energy that is already being used.
An economically sustainable approach is what's needed. Lanzatech's process takes the waste gas from manufacturing, and feeds it into large tanks of his microbes, suspended in liquid. Simpson likens it to putting a brewery next to a steel mill. The bacteria consume the Carbon Dioxide (CO2) and Carbon Monoxide (CO) from the waste gas, add in hydrogen (H) from the liquid, and turn it into ethanol (CH3CH2OH). The other waste of the process happens to be mostly common water, which can be fed back into the tank.
The ethanol can then be used in a number of ways - most commonly it will be sold to petroleum companies to be mixed in with other fossil fuels.