What's clear is Gambino was one of the family's top leaders and not just filling in while other leaders were away. The way Nick Corozzo and his faction are discussed suggests they were in a similar position in terms of influence.
Licata talks about how the "other team" has a guy on the triumvirate as well. Danny Marino was one of the other triumvirate members, but who was the other one at this point? Bartolomeo Vernace had been part of this panel initially in 2008 when Gambino and Marino were first promoted, so I assume he was still part of it. Vernace was close to both the Sicilians and Corozzo faction, so if he was still on the triumvirate I assume the "other team" refers to whatever faction Danny Marino represented.
Licata's comment that "nobody is the boss" of the Gambinos and other discussion about the leadership make it clear that at this time there was no central authority in the family and it was being influenced by several influential factions, not unlike the sort of power sharing we've seen with the Genovese family.
The name Anthony Romano is mentioned. I'd be curious if he is the same one arrested in this case:
https://apnews.com/9b4bbc7d01a3d410c1b7550a01195706
Aside from that, there are the more well-known Genovese Romanos. Carmine Romano was still alive at the time of this tape and living in NJ, would be curious if he has younger relatives on record with the family.
That was one of the more interesting parts of the tapes to me, as you have the Philly acting underboss Massimino doing business with the Genovese family while the acting boss Ligambi didn't want to be involved.