To uninstall AdobeAIR by hand, quit any unnecessary applications (specially applications that might use AdobeAIR). Then delete the following files and folders.
/Applications/Adobe/Flash Player/AddIns/airappinstaller (alternatively remove the /Applications/Adobe folder - first checking that its sub-folders do not contain files other than AdobeAIR files.)
/Applications/Utilities/Adobe AIR Application Installer.app
/Applications/Utilities/Adobe AIR Uninstaller.app
/Users/Shared/Library/Application Support/Adobe/AIR (alternatively remove the /Users/Shared/Library folder - first checking that its sub-folders do not contain files other than AdobeAIR files.)
The following files are in your Home Folder (represented by '~'). You can access this Library folder by holding down ⌥ while accessing the Finder menu Go > Library.
~/Library/Application Support/Adobe/AIR (alternatively remove the ~/Library/Application Support/Adobe folder - first checking that its sub-folders do not contain files other than AdobeAIR files.)
These files were found by scanning the file system before and after installing the latest version of AdobeAIR to see the file changes that were made.