I had Oracle JDK 7 on here also, though not the latest version (the updater ran a day or two ago but it must have been unsuccessful). After uninstalling it, Kindle Previewer runs.
Unfortunately when I install the latest JDK (1.7.0_15), Kindle Previewer again fails to launch. Apple's latest JVM is 1.6.0_41.
KP's Info.plist defines the executable as 'JavaApplicationStub', not 'Kindle Previewer'. So that is what it is trying to run when Kindle Previewer.app is opened. If I launch 'Kindle Previewer' instead, I get this error:
Error: This Java instance does not support a 32-bit JVM.
Please install the desired version.
I tend to think this is KP's problem. Java is pretty good at backward compatibility.
But at least I know how to get it working if I need to.