Here are some instructions that hopefully, will get you to the point where you can change something, build, and run the application to see your change without having to create an entire distribution (which can be slow).
Working with the projects from within Eclipse:
So at this point you've added Ant and Adobe AIR to your path so you can execute "ant" and "adl", you've added a GWT_HOME variable within Eclipse to point to your GWT distribution, and you've edited the build.properties file to point to GWT and AIR. You should have two projects (Asciiroth and Asciiroth Editor) in your workspace that will compile. However, I have never tried to run the build from within Eclipse... you're right, there's an error where Eclipse doesn't get the way the editor build file includes/references the game build file.
Here are the commands I commonly use from the command line:
For the game (from the game/ directory):
For the editor (similar but not the same, but from the editor/ directory):
cd ../game/; ant compile-air; cd ../editor/; ant compile pre-dist; adl src/adl.xml .
And finally, the command that builds up the entire distribution under game/dist:
cd ../game/; ant clean dist; cd ../editor/; ant clean dist