basically do blood sport but with street fighters
do backstory for the characters and then the tournament is like the last hour at minimum
Exactomundo.
It can be a distinctively character-driven story where you have flashbacks to each characters backstory, how they ended up at the tournament.
I would introduce Bison in a subsequent film as someone who was warlord in a war torn country who was trying to take over that country who had an obsession with the occult and that's how he got his "psycho" powers. Maybe tease him as a shadowy figure in the first movie who isn't revealed. He was from Thailand in the game, but that never made any sense to me, it could be some other southeast Asian country. Sagat would just a skilled fighter who believed in Bison's mission. And Sagat recruited Balrog and Vega from previous tournaments; all of them are helping Bison overthrow the government that Bison is a Warlord in.
I would include the supermoves, but I wouldn't go overboard with Hadoukens, hundred hand slaps, and fire-breathing, but I would have it come out in parts. I'd let the actual fighting be as realistic as possible. I wouldn't try to put any scientific explanation to it...it's Street Fighter, it doesn't really work well in live action any way so I wouldn't explain why someone could do a hadouken other than they were just a master of their art.
The tournament is just underground fight with the who's who of the best fighters in the world. All of which are extended by invite only secretively. Hell, I'd use Balrog and Vega as people to personally reach out to all of these fighters in person all around the world. Rather than fight all-around the world, I'd have them come to an island near where Bison was from.