In an unshielded copper conductor the signal travels at 95 to 97% of the speed of light, while in a typical coaxial cable it is about 66% of the speed of light. If your video cable is 2m long then that means that the time it takes the signal to travel down the cable is between 0.000007 and 0.000010 seconds.
Let's imagine that a really bad cable existed, one that delayed the signal by 10 times that amount i.e. the delay would rise to 0.0001 seconds, or 0.1mS.
Given that the picture scan/refresh rate is 50/60 Hz (around 20mS), and the speed of your reactions is between 160 and 190mS, do you think that you could detect a 0.1mS difference in a video cable?
Now, cables that bad simply don't exist. If you find a cable that is 10% worse than typical you would be very unlucky, so you'd be looking for a difference of 0.000001 seconds.......
So no, the video cable brand makes no difference to the delay. It might affect the picture quality, but that's different.