With the help of this video I found their paper. So: In order to compromise the smart card reader, they hooked up their own hardware to it and caused it to perform 10,500 signature operations while they carefully measured the brightness of the LED. For the Samsung private key attack, they're applying in a novel way an already-known timing attack caused by an interaction between the crypto library and the power-saving features of the processor. They threw large numbers of carefully crafted cryptographic operations at the CPU to cause it to change its voltage and power characteristics in ways it's not supposed to, which they then detected at a distance by observing the speaker's LED, which led them to be able to deduce the private key.

It's still extremely impressive and 100% valid research. But, I feel that "if we have access to the hardware / ability to attack the software at length, and in addition we can watch the LEDs, the LEDs can help with the attack operation we conduct" is a little different than what the article made it sound like.