I believe it's called something along the lines of fan labor, as fan fiction is specifically the writing aspect.
Can any of you share any examples of Pokemon fan fiction that aren’t presented as a still image or piece of text?
One of the most prominent in Pokemon are fan games. PokeCommunity has a large community for it, and fan-games are a clear example, branching through to ROM Hackings as well.
Besides that, there are AMV's, which are videos. With music, you will surely not find any sorts of original works as that would not actually be in the fandom. However, there are remixes of the original songs, so that would fit in the category. In addition, there are a vast number of people that enjoy playing the musical scores. Don't forget "filking" but those are more private occasions and they're not as major in Pokemon.
Also, what is your opinion on the idea of fan fiction through video, music or other formats?
I guess, great? Can't really say much here...