"http://games.byond.com/hub/D4RK354B3R/FactionWars

Does this qualify as an entry? I began work on it about 1 day before I created the hub. 3 days before the contest began. What timing."

Unfortunately, no. One of the main purposes of the contest is to get people to make new games. Being that this contest did not encourage you to make the game, no, it does not quality. Sorry.

"As for "third-party sponsors," I'd be happy to chip in an extra 25-50 USD for the entry that I like the most."

An extra $25-$50 would be excellent, but the only problem I can see is you giving it to the entry of your choice. In order for that to happen, you'd have to be a judge (and even judging will go by average score between judges, so the game you like most might not get first), or you'd have to ask all participants to send their entries to you, which would sort of make it its own contest in itself. Now if you wanted to add the money into the pot for the first place winner, or become a judge, we could work with that.