Hello!
When you have the zip file downloaded, you should be able to unzip/extract all the files. This will create a folder in whatever destination you designate for it to unzip to. When you click inside the folder, you should see a .exe file if you're on a windows machine. I'm not totally sure what the mac version looks like - but there should be an application file in the main folder.
If you click on that, it should open the game up!
(Using the itch app will let you open the games from the launcher itself, which is a little easier than juggling the zip files, but it's definitely not required!)
Please let us know if you have any other issues!
~Esh