Not sure what you mean by "jumped right off", but it sounds like the application isn't loading because the download isn't completing properly. That might be why you're being prompted that the downloaded zip file's corrupt - despite the fact that you can unzip it, the files within might be incomplete. I think it might be an issue with your internet or with itch's servers that aren't properly serving the download for you.
Try restarting your computer and router / modem, and then try downloading it again directly from the itch page in a web browser and seeing if it completes the download properly like that; if it doesn't, then try installing again through the itch app itself.