You need to run the editor with sudo (or root privileges). Not sure you can do that with a Chrome app.
You may need to run chrome with sudo to get this to work.
From a terminal
sudo chromium &
But I don't know if there are any security implications that go with this. You may want to only use the app on the browser with sudo and search Internet in another instance.
You might be better off just using a regular text editor.
Edit: Did some searching and chromium won't even run as root, unless you make some changes, so that a pretty good indication not to run as root.
Again, you may want to find a text editor you like that can be installed (not an app). The screenshot looks very similar to something that does work, but the name escapes me
Edit: As discussed it was Brackets that I was thinking of, and you like it but no arm download. I am having issues compiling on my Raspberry Pi due to PhantomJS error, but you may have better luck
Make sure you have node installed.
tar - zxvf node-v0.10.35.tar.gz
Once extracted cd into node directory and do the usual
sudo make install
Now git brackets
git clone https://github.com/adobe/brackets.git
Cd into Brackets directory
Run the following
sudo npm install -g grunt-cli
Then sit back and wait. Hopefully it will build for you. Like I said I'm on a Raspberry Pi, and had issues with PhantomJS, but you may not.