I think we should look into this statement.
So Rukia is a key element to one faction—her survival or execution matters. Hypothetically, if she’s is a player she’s likely survivor. Town aligned at that.
If Ryoka is a faction, that means they’re at odds with town over Rukia’s execution. Which means the Ryoka factions’ win condition would be making sure Rukia survives. Possible for Maf but sounds unlikely.
Moving forward—in the arc itself, the Gotei 13 and Ryoka were at odds because of Aizen. That means to say, Aizen and his faction likely have killing Rukia as a special win condition (as per the manga where Aizen wanted Rukia executed to extract the hogyoku from her).
So, if we have three factions, this is how they should align;
Gotei 13 — Eliminate all threats to town.
Ryoka — Protect Rukia Kuchiki.
Aizen — Kill Rukia & eliminate town.
So if we do have Ryoka and Gotei 13, they likely don’t directly interfere with each other. Considering the Soul Society arc focused on twists and betrayal, two factions that needlessly fight seems right for this Mafia.