Right, stared at GNPs and food/production numbers while I ate my lunch and I have an alternative hypothesis.
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T0: TEAM settle on a normal tile & work a floodplains (3/0/1). Their GNP is 19. We know this from the T0 demos after they settled but no-one else did. They start to research Hunting (or don't select a tech, it's irrelevant which for the GNP).
T1-T5: TEAM switch to working a 0c tile (probably 1/2/0, extrapolating from the production numbers knowing that Gillette are the only ones with 1 production on this turn. Alternatively, they're the guys with the 4 yield tile available - was it forested deer (2/2/0?) we speculated? That'd fit with going Hunting first). Still researching Hunting, their GNP is 18. Someone else has the top GNP of 19 - Pirates or Menagerie.
T6-T10: TEAM have now finished Hunting at end of last turn & switch research to a tech with a single pre-requiste (possibilities are Pottery (I don't think The Wheel counts for pre-req calculations, is this true?) or Archery, I'd guess Pottery). They also work the 3/0/1 tile again. This puts 65 beakers into Pottery & they'd need 4 more turns to finish it at this GNP.
[Note that if TEAM worked a 3c tile "for real" and swapped off it each time so we couldn't tell, then it's possible they researched Mining finishing end of T5, and so could be researching BW for a single pre-req tech.]
T11: TEAM switch research to AH (for which they have 2 pre-reqs) and switch to a 0 commerce tile (which from the other numbers can't be 1/2/0, could still be 2/2/0). Their GNP is 22.
T12: TEAM meet the second one out of Gillette & Pirates this turn, and have switched back to the 3/0/1 tile. This gives them a GNP of 24 while researching AH. They'll need 8 more turns to finish it at this tech rate.
If that's all true, I've no solid idea what Menagerie are doing

It might involve tech swapping, in which case I can't really make guesses about what techs they're researching. Another possibility is that they like us are researching BW. They've probably got between 120 & 156 beakers invested in whatever it is, depending on GNP rate.
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Plako's original hypothesis is for Menagerie to have settled on the wines and I can't make the GNP of 24 fit for Menagerie:
T0: Menagerie not settled yet.
T1-T5: Menagerie settled on Wines (or another 3c tile), and didn't put beakers into a tech or researched a non-pre-req tech. Either they had a GNP of 19 (working a 1c tile) or a GNP of 18 (working a 0c tile). They accumulated between 60 and 65 beakers during these turns - enough to've finished Fishing if they were researching that, but not enough to finish any other non-pre-req tech available. A guess here is Agriculture.
T6-T10: Menagerie work a 1c tile, and research a tech they have a single pre-req for, ie Bronze Working, Masonry, Animal Husbandry, Archery. BW or AH seem most plausible to me. They accumulate 75 beakers during these turns, and would need another 7 turns to finish BW at this rate (or 5 for AH but see next).
T11: Menagerie have met both Gillette & Pirates & are researching AH working a 1c tile. Their GNP is 22 by the time we see it (ie after Gillette finish AH).
T12: I can't account for the GNP of 24 if I'm trying to make it Menagerie on Wines - the only way I can make the numbers work is if they're researching a tech with 2 pre-reqs that 1 or less known civs have and working a 1c tile. Which isn't possible with the techs they know. So you'd have to swap in the TEAM one from the hypothesis above.
If this is what's happening then TEAM have accumulated between 60 & 66 beakers since researching Hunting & these are invested in one or more non-pre-req techs (Fishing, Mining, Mysticism). And they've put a single turn of research into AH.
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I don't much like either one, they involve too many ifs & unknowns. But I've written them out as much to see if anything later contradicts them as anything else