Let's start by marking some points:
D and G are static. We control by rotation of FG about G. We can drive that rotation from a custom value if you want, but the only masterRot I see is the input to a GN modifier. I guess we could drive it from the value of that input.
The structure isn't fully defined yet. To define it, we need to create a bone from F to E, as the structure in your linked video uses. We should also notice that ACD forms a triangle, where the angles can never change, so we don't really have to worry about AC.
Start with GFCDA:
FC and CD take part in an IK chain, targeting the free bone at D. (This point will remain static; I have parented to "root.") Both bones are IK locked in all but one axis. FC has inherit rotation disabled so that rotation of its parent, GF, won't flip it out when it rotates too far. DA is just parented to CD. (Remember, CDA is a triangle, it can never change angles.)
We can do the same with GE and ED now-- it's just a 2-chain IK, targeting the same, static IK target:
Again, locked in all axes, and DE doesn't inherit rotation.
Now we've defined the position of A and E, there's only one place that B can be:
AB and BE form a 2-chain IK, targeting the head of ED because that's convenient. Still locked in all but one axis, although that doesn't really matter; but here, we actually want AB to inherit rotation from its parent.
Now we can create the driver for the rotation of GF. I'm pointing all bones' Z axis at my camera, so we'll change it to a ZXY Euler and drive its Z rotation from masterRot:
You can map that however you'd like. As is, that's the rotation in radians.
One more thing to do. Let's fix those bones that aren't inheriting rotation so we can actually rotate the structure about. We'll reparent them to root, re-enable inherit rotation, then give them a copy location constraint, world->world, targeting their old parent's tail-- that is, acquiring the position of F. Any constraints we put on IK bones will be evaluated before the IK is evaluated.
And, I'll make a few copies with different master_rot inputs as proof that it's working:
