It does not matter what permissions are on that file. You need to have write permissions on the directory that contains the file.
(You can even remove files not owned by you if you have write permission for the directory. A confirmation question will appear and by answering with yes, the file will go away.)
So while impersonating the root user will remove the file, you could do that by your own if you could write to the file's parent directory.
Could you list the permissions + owner for that?
On the reappearing problem:
sudo crontab -l to see if there are any cron jobs for root, and include the output in your question.
Your response was:
* * * * * touch /home/chimp/Desktop/hardcore_porn_xxx
Your output states it is a cron job.
Now please execute
sudo crontab -e, pick your editor (e.g. mcedit) and delete the whole line containing
touch.... Exit the editor, remove the file with any method and wait. It should not reappear anymore.