So, I'm referring to the games on the front page, meaning I can't get in touch with them? If I can, do I need to give something in return?
Viewing post in My game in first page
You can, but it may even be counterproductive.
There are several posts where they talk about how Itch doesn't accept payments or anything similar to promote games and if you try to search for it with that sole purpose, you may be ignored.
Make sure your game and page are of good quality and promote the game. You can promote it and mention Itch on twitter for example to get their attention and if the staff likes your game, they may promote it.