I'm a little confused about what it takes to have your game listed these days.

1. The game must be truly your own, not simply edited from a "codebase"; i.e. it must not be a "rip".

This one is fairly obvious. If you didn't write the source, you don't get to use the source.

2. The resources used by your game are original work or are used with the permission of their respective authors.

This one I don't get. Because apparently it's okay use images from games released by the IP owner.

Pokemon games are the most notable offenders of this. Also there's Naruto: Eternal Memories, and I'm sure that the DBZ games have offenders too. I'm also kinda sketchy about the Yugioh games using the actual card images too.

I guess it's okay as long as you don't rip icons from another game? But if they use the same icons, and you both got them from the same source, technically neither of you ripped the other, but you're both using the same content? I'm so confused.
If you haven't figured out BYOND doesn't even know what their own rules mean by now then IDK what to tell you. Many anime games violate the second rule yet get listed in fan games.
Those rules only apply to being listed in the "All Games" section of byond. If you click "Anime" or one of the other filters, then they'll appear normally. They also won't be featured if they break any of those rules.

You can check yourself if you'd like: all or mostly originals. a filter for the games list, all anime fangames are now shown.

Byond doesn't ever list anime games and the like, but by clicking those links you're doing a filter search, which results in those games showing up as they're explicitly being searched for.

Looking at that list I don't see any that I would immediately suspect have images from GBA or NES games. However, I do see games that should probably be listed as fangames.

Seika SE
Bejeweled Online

Not to mention the various Minesweeper games and Chat games that I personally feel should be limited (after all, don't want to list the same content all the time eh?)

But I suppose you're right.
This one I don't get. Because apparently it's okay use images from games released by the IP owner.

No, this is still copyright infringement. Partly, I feel this rule is there to cover BYOND's ass. Likely, you'll be fine until BYOND gets a C&D, as with DBZ.
I know a moderator who will list anything for me, so yeeeeaaaa.