Old Properties (Pre 2016)
In short, it's a great big (and often conflicting) mess but hopefully one that should improve over the next few years with Capcom taking a far greater interest in creating a cohesive 'universe', according to the 'director of publishing' for Udon Publishing, the official publisher of the current Street Fighter magazine.
Matt Moylan: If it was in a manual maybe or even in a Japanese [manual]. Some people say if it's in the games it's canon but even then like a lot of the
games contradict each other. A lot of alpha games have like 'what if'
endings which obviously even within the game can't all make sense so I
mean it's hard. It's really tough to say what is what's canon for
street fighter that's why I like the word 'lore' is it can bring in and all these different ideas from different continuities where this [is from] the mangas or the comics or the games or the anime.
Maybe even you even asked a Capcom about this before, I know right now
they're kind of trying to make an effort since they started the
games again
Transcript edited for ease of reading
New Properties (post 2016)
According to the creator of Street Fighter: Assassin's Fist and Street Fighter: Resurrection Joey Ansah, there's now a strict canon that must be adhered to. Character's back-stories need to be observed, even where that canon is "cartoony" or makes zero logical sense. Unfortunately there's no series 'bible' that can be referred to, so the final arbiter of canon is Capcom's liaison with the games and tv show developers.
How much liberty do you have when you're writing the story, or do you
mostly have to stay within the parameters of Capcom’s existing
universe?
Joey Ansah: My kind of boat is about being true to the canon. I think what pissed a lot of people off about the two movies that came out is that they
completely went off-piece and took huge liberties. They were turning
it into something else that's no longer Street Fighter. It's a vague
interpretation of Street Fighter. It goes without saying that adhering
to the canon is a must. And sometimes the canon that Capcom have
created is f%#king ridiculous. I have to be quite inventive to make
that work in a believable, intelligent way. That's part of the fun,
part of the challenge. Elements in the Street Fighter story are quite
cartoony and not very deep.
Capcom trusts me now, which is nice. Resurrection has been the hardest
to do, because at least with Assassin's Fist, there have been anime
series and official comic books that have told elements of Ken and
Ryu's early years, so there is at least some established canon for
what has happened. When I tried to do Resurrection, which is like a
prologue for Street Fighter V and set after Street Fighter IV, there's
a big question mark for what has gone on there.
...
There were things I wanted to put in that I had to change to fit the
canon. It was hard because it's not like Capcom gave me a special
story book saying here's all the new canon, six or seven months before
the game comes out. I had to ask questions and they would say, "Yes,
this is canon" or "No, the direction you're going in is counter to the
canon." They wouldn't really give specifics.
We chat to Street Fighter: Resurrection director and writer Joey Ansah
Joey also offered some additional description of what Capcom consider canon in the Street Fighter universe; the official games, the prologues and epilogues of the games, but not the anime shows, cinematic films or crossover games.
This is multi-generational story. We know Ken and Ryu after two
decades fighting alongside them. But outside combat, how do you get
into their headspace?
Where does one begin? ...We wanted to create the definitive backstory.
The story in the Street Fighter universe is very fractured. You had
Street Fighter and that tournament, Ryu beating Sagat at the end, so
you've a bit of narrative there. The anime then retro-fitted in that
[Sagat] got the scar from Ryu. Then they retro-fitted that in Super
Street Fighter II Turbo, Akuma comes in. And they say "okay, he killed
Ryu and Ken's master, and was that master's brother". Then there's a
long time before Gouken, Ryu and Ken's master, is given a name. So the
story's been retro-fitted as its moved forward.
So we've tried to take what's regarded as canon by Capcom, what
appears in the prologues and epilogues of the games. The
Capcom-endorsed and sanctioned animes, although they are official
Capcom stuff, they're not regarded as canon, all of what's in there.
Street Fighter: Assassin's Fist Interview