Hi!
You are correct. That directory will only allow the user root to write to it. You should change the permissions to allow all users to write to it, or change the owner to your normal user accounts. The command for the first is sudo chmod 777 echo-nest-remix-examples and the second is sudo chown (your username) echo-nest-remix-examples. You can of course choose both.
The reason running your script under sudo game that error is that sudo typically deletes all but an approved set of variables from the environment used to run the desired command. It can be configured to leave the ECHO_NEST_API_KEY variable in the environment, but it's much safer to not run things as root when possible.