Street Fighter's story is no different quality-wise to the stories of other fighting game franchises, and that's actually not really a good thing to say, but still...
Street Fighter's story is neither boring nor nonexistent, it has existed since the Alpha series but it has always been harder to follow because it is told in a particularly disjointed way across titles that are constantly jumping all over the timeline, and so most people barely even know what's going on exactly in the narrative. Tekken, Mortal Kombat and Soul Calibur might deal with their chronology in a much cleaner way and it's easier to get a summary of what happened last time, but in the end they're as much of a silly mess as Street Fighter.