The NYT is being disingenuous in presenting this as VW detecting the EPA test cycle and doing something to cheat. I think they've confused open loop and closed loop engine operation.
VW's 4-cylinder engines which failed the EPA tests are all turbo engines. Turbo engines run hotter than naturally aspirated engines and so, they produce more NOx, since it's one of the high temperature byproducts. In fact, EGR (exhaust gas recirculation) systems inject exhaust into the intake to lower combustion temperatures and NOx output. All engines do this, turbo or not.
Whatever NOx makes it out of the engine can be catalyzed in the catalytic converter if there is enough O2 for the catalyst. All the engine's intake air and temperature sensors, and pre-cat and post-cat O2 sensors exist to balance the gases coming into the catalytic converter to optimize the catalytic reaction.
When the engine is using all of these sensors to fine tune the amount of air, fuel and EGR to maximize catalyst efficiency, it's running in something called "closed loop" mode. The sensors and inputs work in a closed loop to balance the system. This is what happens when you're cruising on the highway or driving around at relatively fixed throttle.
Give the car a lot of gas, and something else happens. All of a sudden, a LOT more air enters the engine. The sensors can't change reading fast enough (mass air flow sensor, for example) or their readings are now out of the sensor's useful sensitivity band (for O2). The engine code knows that sensor capabilities have been exceeded, and it goes into "open loop" mode. In this mode, rather than using sensor readings, the engine reverts to pre-programmed maps, usually indexed by RPM, throttle position, engine load, and boost level. These maps are designed for relatively clean combustion and engine safety, but they will not generate optimal catalyst input gases, and so, the catalyst efficiency drops off tremendously. Furthermore, performance cars will often burn rich (too much gas for amount of air) in order to prevent engine destroying pre-detonation.
Most of the EPA test cycle will happen in closed loop mode. Most high throttle acceleration or "fun" driving will happen in open loop mode. There's the source of the discrepancy between EPA test cycle and real world driving. VW got caught, but every car does this, as we don't have wide-band, high-rate sensors yet at a price point even close to where it would need to be for consumer cars.
(Next time you see someone racing off from a stop light, in pretty much any car, watch the exhaust pipe, you'll see dark smoke. I guarantee you they're running rich in open loop mode).