I think the reason that they are staying close together is for physical support...so one can't knock the other down. I am not certain but I would think that rising from a lying down, or from being knocked down would be ackward and perhaps difficult for a giraffe...
Most times females that are herd animals don't fight for the right to mate. There is a male who is over the entire herd.
If you were to google giraffes fighting, then you could see or read about how male giraffes fight for mating/feeding/territory rights...