Magic Quotes, generally speaking, is the process of escaping special characters with a '\' to allow a string to be entered into a database. This is considered 'magic' because PHP can do this automatically for you if you have magic_quotes_gpc turned on.
In your case however the issue is caused due to the fact that data has been sent to the browser before the session_start() was called. This is quite a .. developer mistake in my opinion, but hey

I'm no developer so I can't really say it.
To correct this small issue I've added the following line at the start of the installer:
ob_start();
and at the end of the file, I have therefore added:
ob_end_flush();
which buffers the output and send it at once instead of sending each data unbuffered. Now it seems that the installer works fine.