Jimmy the file permissions for their User account have become compromised. You can find an example of the errors found within your posted log below:
06/10/14 15:44:38:274 | [ERROR] | | OOBE | DE | | | | 42830 | DF037: Unable to delete directory "/Applications/Adobe Illustrator CC". Check and correct folder & parent directory permissions and then try again.(Seq 16)
06/10/14 15:44:38:274 | [WARN] | | OOBE | DE | | | | 42830 | DW063: Command ARKDeleteDirectoryCommand failed.(Seq 16)
06/10/14 15:44:38:318 | [ERROR] | | OOBE | DE | | | | 42830 | DF037: Unable to delete directory "/Applications/Adobe CC Apps/Adobe/AdobePatchFiles". Check and correct folder & parent directory permissions and then try again.(Seq 17)
06/10/14 15:44:38:319 | [WARN] | | OOBE | DE | | | | 42830 | DW063: Command ARKDeleteDirectoryCommand failed.(Seq 17)
06/10/14 15:44:38:334 | [ERROR] | | OOBE | DE | | | | 42830 | DF037: Unable to delete directory "/Applications/Adobe CC Apps/Adobe After Effects CC/Presets". Check and correct folder & parent directory permissions and then try again.(Seq 18)
06/10/14 15:44:38:334 | [WARN] | | OOBE | DE | | | | 42830 | DW063: Command ARKDeleteDirectoryCommand failed.(Seq 18)
06/10/14 15:44:38:334 | [ERROR] | | OOBE | DE | | | | 42830 | DF037: Unable to delete directory "/Applications/Adobe CC Apps/Adobe After Effects CC". Check and correct folder & parent directory permissions and then try again.(Seq 19)
06/10/14 15:44:38:334 | [WARN] | | OOBE | DE | | | | 42830 | DW063: Command ARKDeleteDirectoryCommand failed.(Seq 19)
06/10/14 15:44:38:334 | [ERROR] | | OOBE | DE | | | | 42830 | DF037: Unable to delete directory "/Applications/Adobe CC Apps/Adobe". Check and correct folder & parent directory permissions and then try again.(Seq 20)
06/10/14 15:44:38:334 | [WARN] | | OOBE | DE | | | | 42830 | DW063: Command ARKDeleteDirectoryCommand failed.(Seq 20)
For information on how to adjust the file permissions on the affected directories/folders please see Error "Exit 6" or "Exit 7" | Install log | Read, write, system file errors | CS5, CS5.5 - http://helpx.adobe.com/creative-suite/kb/error-exit-6-exit-7.html.