are you monitoring the gpu temperatures?
with HWinfo64 for example?
maybe it's temp related thats why reinstalling drivers make them go away for some time (because gpu gets cooller) and reapears when you game,

really wierd issue and if software changes like reinstaling drivers and system doesn't help it must be hardware related (temps perhaps?) or some vbios bug...

Try using Display Driver Uninstaller - it will whipe all previous display drivers leftovers (registry also gets cleaned from them). Get newest version here:
http://www.guru3d.com/files-details/display-driver-uninstaller-download.html
then download and install newest geforce driver

If that doesn't help, 3rd RMA and this time expect to get new unit or motherboard replaced.

I've also had a black (sometimes green against black backgrounds) single line of dead pixels on the left side of my G751-JY, purchased through newegg. My first one did it out of the box. I RMA'd it. Now on my second one (acquired in June), it was initially intermittent, as I could get it to go away by partly closing the lid on my laptop and then fully extending it again. After one day in a secure laptop bag, it's been a permanent fixture of my display. Asus's quality has been garbage of late. I ultimately got a full warranty refund for the power problems I kept running into with the G750, and I only went to the G751 because of all the hooting and hollaring I'd heard about its "awesome performance" with Elite and Star Citizen. Sure, it performs great; and I should be happy, because while at home, I port the screen out to an external monitor with no problems. However, I'm also a Navy reservist. Both my civilian and military careers make me travel often, and I would like not to be distracted by a bloody line of dead pixels on my screen.

I'm sick of RMA'ing things to ASUS to get the same issue repeated in each repair/replacement. Clearly, from what the OP said, I'm not the only one who keeps experiencing their "fresh wipe and return" policy of repair. I'm about to change the screen myself, should anyone have a guide on how to access the lid.

Frustrated and over it. For computers with such great gaming performance, they sure have the worst Quality Assurance I've ever seen in a brand.

When you get the laptop back from RMA is it mentioned what kind of repairs have been done on laptop? Also try changing the refresh rate on your laptop once if the vertical lines worsens or not. My laptop had the same problem but it was fixed when I changed the refresh rate from 75 Hz to 60 Hz. Eventually I returned it as it had USB problems and overheating but yeah try changing the refresh rate.

Having worked in electrical retail/IT for some time, vertical stripes on the screen to me usually indicates a faulty screen or possibly a loose cable going to it. The issue may come and go due to the nature of laptop screens (i.e they move to open & close) but if I were you I'd be RMA-ing this in.