The exact rules for why one game is indexed and another isn't are kept secret by the staff, but what we know is roughly the following:
When you create a game, it should appear indexed by default. However, when you publish the page or make a change, an algorithm runs that, based on several (secret) criteria, can determine that a project is suspicious and needs to be manually reviewed by a staff member. At that point, your game will be removed from the index and placed in a queue for a staff member to review. If they determine there's nothing wrong, they'll reindex it.
Therefore, not every game needs to be reviewed by the staff. We don't really know how many games are indexed directly versus how many require manual review, but if you look at the "Most Recent" page, you'll see that many games are indexed as soon as they're created, even by new accounts.
From what little we know, paid games, especially downloadable ones, are more likely to require manual review by the staff, but there isn't much more information.
When you upload a game, it can happen that it's indexed immediately, but if you're unlucky enough that the automated algorithm determines that your project needs manual review, you're forced to wait patiently until the staff has the time to review it. This is why bizarre things like what you mentioned can happen: the original project of a real person who put in the effort gets deindexed while an illegal copy gets indexed.