The rules have been revamped a few days ago, most notably making use of the Main Rules.

Emulator rules have been specified further, requiring you to disable the "Speed up Disc Transfer Rate" as it pushes loading significantly beyond the capabilities of any legitimate version of the game.

Unofficial ways of running the game aside from emulators are now allowed as well, like Open PS2 Loader (OPL). Since loading are again sped up notably, timegates were put into place to make sure OPL does not lead to times that are impossible to beat on official hardware. The timegates are up for debate, but any slower runs are perfectly okay to be accepted on the board. Emulators are also affected by this rule. Should timegates seem unreasonable, feel free to bring it to my attention and I can adjust them as needed.

Emulator runs are now allowed on the leaderboards.

You can use Dolphin 5.0 to play the Wii version. Note that in order for a run to be eligible, the emulator must be configured in a way that makes the game crash/freeze when approaching the gates on the Frozen Coast when retrieving the Uka bone during the late-game. Dolphin loads slower than Xbox 360 and Wii U, but outperforms a regular Wii and a PS2 by quite a margin.

Further, you may submit runs emulating the PSP version using PPSSPP 1.12 or higher. Due to some changes and patches exclusive to the PSP version, it is unlikely that any outrageously fast runs can be done either on emulator or on a real PSP.