Those appear to be a pretty good launchs. No unusual bouncing or bobbing of the front or rear suspension. No apparent wheelspin.
I am guessing that you do not have a spool in the rearend. Without a spool you will nearly always get a slight difference in torque applied to each rear tire, even with a limited slip differential. That difference in torque will cause the vehicle to slightly steer to one side or the other. For guys that have been driving muscle cars on the street for years with that "wiggle" the correction in the steering wheel is so second nature that I'm not surprised that you are not aware of making that adjustment. I don't think it is a problem untill you start pulling the front tires off the ground at launch. Then it will be a real important problem to fix or else you will end up in the wall right at the launch. A rebuilt differential would help, but a spool is the best solution for on the track.
Your rearend might also be slightly misaligned with the car. Or perhaps a bad front tire alignment causing you to stage at a very slight angle. So could slicks that have different air pressure, or different rollout circumferences cause this. Or even just a minor variation in traction of the track from side to side. But in this case I think the most likely cause is the simply the limited slip applying differing torque to the each slick.
All that said, you should video other fast cars from the rear at the launch. You will find that many of them have some wiggle as they go launch and go down the track, depending on how their suspension is reacting and the traction under each one of the slicks. And even defects in the track surface can cause a car to move around.
