It says that when you upload a game you can choose the "unlisted" option, but on the create section, there is just a section to put in your game file, and a button that says upload. I need to make sure I don't accidentally make my game public. Thanks :)

I think it happens automatically. Only people with the actual link can play it.
Then you need to make an active choice to "open" it to the public. =)

Thanks CheeseMyBaby. So, once you uploaded it, is there an option to open it to the public? And, is it pretty straight forward how to replace one version of the game with an update as your working on changes?

once you uploaded it, is there an option to open it to the public?

Affirmative.

If you made your game online, you will see this on your 'Create' page:

If you made your game in the desktop editor and submitted it to the site, you will need to click on the 'Published' tab to see the game in the list.

Click on 'View/edit game listing', and you will be taken to this page:

Click on 'Edit this listing', and you will be taken to this page:

From there, you can upload a new file to update your game, or you can change "Who can access this game?" to "Everyone" to change it from a private listing to a public listing.

If you decide you'd rather it not be public afterwards, I think you can go back in and set it back to "Only people I give the link to".