This is not a bug per se. ShiftIt 10.6 actually works on OS X 10.9, but there are some obstacles. You could consider this a documentation issue.

First, you have to re-enable the Accessibility API. In OS X 10.9, accessibility has to be enabled per application. Under System Preferences → Security & Privacy → Privacy → Accessibility, select ShiftIt.

Second, I found that after upgrading from OS X 10.8 to 10.9, you have to reinstall XQuartz. (I had XQuartz 2.7.4 installed under OS X 10.8, but after upgrading to 10.9, ShiftIt complained that it was missing.)