What you're looking at isn't the old, 2012 Kawasaki ZX-6R. Well, it is, but in Japan, they're calling it the 2013 "race only" model. The solution to homologating the now-636cc bike for 599cc supersport racing (in Japan at least)? Just sell racers the old bike. Since the '13 only updates engine size, electronics and bodywork, that's relatively easy.
Here's a picture of a 2012-model ZX-6R pulled from Kawasaki's website. Compare it to the bike up top, that image was pulled from Kawasaki Japan's new page for the 2013 "race only" model. Then compare specs between the two. Where the 2013 has a 67.0 x 45.1mm bore and stroke and a 12.9:1 compression ratio, both the 2012 production bike and the 2013 "race only" share 67.0 x 42.5mm and 13.3:1 numbers.
Here's the 636cc 2013 Kawasaki ZX-6R. Note the different headlights, indicators, exhaust etc. Despite that capacity change and the addition of traction control, it's a relatively minor facelift.
And the similarities between the old bike and the "new" race model continue away from the engine too. Where the 2013 production bike has a rake and trail of 23.5 degrees and 101.6mm, the 2012 and the race bike share 24-degree and 103mm figure. That identicalness extends even to the curb weight: 423.4lbs for the 636, 421.2 for both the 2012 and the new race bike. Kawasaki is literally selling the old bike as a "2013" specifically for homologation purposes.