Is Aperture installed in the "Application"s folder and simply named Aperture? If not, move it back to "Applications". Did you buy Aperture from the App Store or as a boxed Retail version?
Relaunch the App Store and sign in with your Apple ID (in the Store menu). Reload the "Purchased" page of the App Store. Do see Aperture on the Purchased tab or perhaps the "Accept" portion of the "Purchased" page? If in the "Accept" portion, accept it to your AppleID and install it. Else look again at the Update page.
For some forum members the update did only appear until after setting the primary system language to English and rebooting the Mac. This bug is supposed to have been fixed with the update to 10.9.1, but try it, if all else should fail.