Since you are running still Aperture 3.4.5 and your current Aperture version has not been bought from the App Store, you will see it on the updates page, but not on the purchased page. Only the update to 3.5.1 will convert your serial-number license key to an AppStore license and show Aperture among your Purchases.
To be able to update Aperture to 3.5.1, consider to upgrade your old machine to Mavericks. Once you see Aperture 3.5.1 in the Accept part of the Purchases tab, it should show on your new Mac as well.
My previous post should have said outside the App Store, sorry.
Alternately: Do you still have the downloaded installer? Then copy the serial number from the "About" panel on your old Mac. "Aperture > About Aperture".
If you do not have the installer, copy the Aperture application over and try, if it will launch. Enter the serial number. Then update it to 3.5.1. and accept it.