The ZIP file in the dist directory is just for convenience in case multiple artifacts are published on a server. This gadget file (wakatime.xml) is self containing (everything is inlined); easier to handle.
At the moment it's a bit confusing; the new UI doesn't seem to be complete; some tasks had to be done with old one.
The gadget doesn't have to be public. If you've finished the process with the dev console you'll see it in your Hangout widget list (dev category).
The URL that I am using points to the raw Github file (https://raw.../wakatime.xml). This is just for testing. Ultimately it should be hosted on a proper server.