Not all characters belong to any of the factions.
This, obviously.
But I have to say, I don't think I'll ever understand how NRS arrived at the 5 factions they have for MKX. Sub-Zero gets a faction but Scorpion doesn't? Kano and Tremor get a faction, but Kotal/Erron/Reptile/Ferra/Torr/Ermac/D'Vorah don't? OK, they want to focus on the "classic" factions, well where's the love for Mileena/Goro/Baraka?
I just don't even know.
The new Shirai Ryu died out in the comic which is why not it's not a faction.
By that logic, Goro shouldn't have four arms in MKX.
There is a time period during the events of MKX, which might even be shown in Scorpion's or Takeda's flashbacks, in which the Shirai Ryu is rebuilt. That's plenty reason for it to exist as a faction.
Don't assume it's dead forever.The new Shirai Ryu died out in the comic which is why not it's not a faction.
Kittelsen has the arm thing covered. https://twitter.com/kittelsen/status/585142760161812480
Also https://twitter.com/kittelsen/status/584789033689026560