[google-api] This IP, site or mobile application is not authorized to use this API key

In addition to the API key that is assigned to you, Google also verifies the source of the incoming request by looking at either the REFERRER or the IP address. To run an example in curl, create a new Server Key in Google APIs console. While creating it, you must provide the IP address of the server. In this case, it will be your local IP address. Once you have created a Server Key and whitelisted your IP address, you should be able to use the new API key in curl.

My guess is you probably created your API key as a Browser Key which does not require you to whitelist your IP address, but instead uses the REFERRER HTTP header tag for validation. curl doesn't send this tag by default, so Google was failing to validate your request.