The new study says we’re about as far from chimps as we are from chickens.
No it doesn't, it says the MSY gene shows a rate of difference between 6 million years of change between man and chimp as it does with 640 million years of change between man and chicken. This is a sub fractional difference and doesn't reflect the entire genome and really only represents what has changed over time- something accelerated the change in the MSY section of the Y chromosome in chimps.
In layman's terms, it is like looking at a Camaro, a bicycle, and a Ferrari, and finding that the way one component in the transmission is bolted more similarly in the Camaro and bicycle than the Camaro and Ferrari. It doesn't mean the Camaro is now more similar to the bicycle than the Ferrari, it just means this one bolt is.