Recently, there's been some good, and new, engines out there that allow developers to create their own .IO game and publish it online. I made my own game with it and was informed my itch.io game successfully publish, but can't find it anywhere! The game I want to put out there uses a link to the website only, but the itch.io submission options did not allow links as a valid submission...

Is it possible for you to allow people  some other option to submit games (like website links) instead needing files to download? Forgive me if there is a reason against, I am new and could not find much information about this issue

The best approach right now is to create a page that in the description contains a link to your game. We are experimenting with a iframe embedded version of the game page, but sadly many IO games do not have https support which breaks our security requirements.