I downloaded the Aptana_Studio_Setup_Linux.zip package, unpacked it and run ./AptanaStudio. It starts fine, but reports one problem:
The embedded browser widget
I happened to come across this: https://groups.google.com/forum/#!msg/xmind/5SjPTy0MmEo/PbPi0OGzqPwJ
Which advised running:
sudo apt-get install libwebkitgtk-1.0-0
should solve the problem. It worked for me so I figured I'd share here.
FWIW, I ended up here while trying to get the Play! Framework working on Ubuntu 13.04. using the Scala-IDE. So far, everything seems to be working...