So I have the game and can play it via the Dios Mios Wii booter would a run using this still be considered valid? Or if I was to use Dolphin EMU on a PC?

If it's not run on a version officially released by nintendo, ie; backup loader, emulator, custom hardware, then it's considered emulator.

Alright thank you

What Guggy said is not accurate, the emulator leaderboards are only for runs done on Dolphin. USB loading and the like are not allowed on our leaderboards at all. That being said, emulator is also discouraged and I would strongly suggest you play with an official disc if you want to run this game even somewhat seriously.

What I said is a general guideline. I never said it was the rules for this game /shrug