What command did you use to try to install it?
The error is because the user running the command doesn't have permission to write files in the location it's trying to install in.
It looks like you are trying to install it as a global module (by including -g in the command).
But you'd typically want to install the module in your Node-RED user directory - .node-red in the users home directory. Node-RED logs the location of the user dir its using when it starts up.
In that directory, run: npm install node-red-contrib-zip
