I have done my first speedrun of the game but i use and emulator so i dont have to buy a capture card, why are they banned?

Emulators for Wii games are noticeable to have inconsistent time loads, whether slow or fast. Because of that, it is up to the speedrun community and its moderators to decide if they should include a different category + some restrictions for runs performed on an emulator or ban emulators.

Games like Wii Sports and Wii Party allow emulators on their leaderboards, but they are hidden by default.

If you’re able to play on console then it’s perfectly fine to record with a phone camera pointing at the screen, as long as you can see the screen for the run (or streaming so you don’t run out of recording space on your phone). Lots of people do that even in top runs.