ID:2093533
 
How do I go about getting my game to be published? Is their a submit form or something?
I think you hover over your username in the top right and then click Publish Games.
I don't think that would list my game as "Published" under the Published Category via Pager.
Marking your game as visible automatically puts it in front of the moderators to look at. They can make a simple yea/nay decision on advancing the game to Published from there.

If your game was previously given a nay, it may not show up there, but you can reply to any admin feedback (or just post in the feedback thread) if there's some new information, and it will reappear for the moderators to look at.

Gotta say though, neither of the games I see in your list are gonna get the Published stamp, for rather obvious reasons.
Perhaps I can make a few changes and re-apply in the future?
Yeah, that would make sense. They both are clearly fangames, and that's the big problem. Divesting of that in favor of original material will cleanse them; an original game should be fine for the Published section.
Just checking in to see if I've done things right: http://prntscr.com/behjv0