The nodes could for example look like a mix between water towers and electrical transmission towers. The tethers or rope drives would then be raised from the ground, like suspended transmission lines are. The topmost sheaves could be for the ground stations surrounding this node and could go around an upright, vertical axis, static, cylinder, to reduce their inertia. The individual sheaves would probably have their own bearings to allow for independent rotation. The cylinders for lines coming from nodes further out could have a vertical or horizontal axis I think, perhaps depending on if the nodes are in line or not.
Assuming you have a number of tethers or rope drives coming from a node, in the generator station you could place the drums for them in line with the tethers, one behind the other, their axes perpendicular to the lines: [] [] [] [] [] [] — [drums: [], generator shaft: ), or slightly staggered to stagger the transmission from the drums to the generator shaft.
Additional tethers from additional nodes could then come into the generator station parallel to the other tethers and go to drums that connect to the same or different generator shafts, resulting in a (staggered) grid of drums.
The transmission from the drums to the shaft could be something like a CVT that connects to one of two gears, depending on if the line is reeled in or out. Like this there would still be a sudden direction change of the drums when going from reel out to reel in, so you’d need to find a solution for that, in the likely case that is a problem.
One wonders if it is a problem if the kites don’t pull exactly the same. I think perhaps not, just like it isn’t much of a problem if reindeer don’t pull exactly the same on a sleigh. The CVT should also optimize reel out speed for an individual kite (train).