I'm having the same issues (minus the artifact space invaders) on my new ASUS ROG Strix 2080 Ti.
The Nvidia driver nvlddmkm crashes every few minutes under any kind of load on a regular basis. It does recover but obviously it makes gaming useless. Games lock up for 3-5 seconds and then resume as if nothing happened.
The card itself is overclocked by default from Asus, and I've not touched that myself due to hearing rumours about issues with it. There are suggestions to lower the OC manually, but I don't want to affect the warranty with that.
I've completely uninstalled the graphics drivers using DDU, reinstalled, tried all versions since the ROG Strix 2080 Ti came out but nothing seems to work.
Re-seating physically doesn't help either, and an old Nvidia/Windows registry fix to increase the timeout value on the driver crash doesn't help and that had a lot of promising feedback.
Contacted ASUS with evidence and screenshots, and immediately they've asked me to RMA, via OC UK. Guess I'm going to be without the card for at least 2-3 weeks now. Just wondering now whether to bother getting another replacement 2080 Ti or drop to a 1080 Ti? Any suggestions welcome. I'm not happy having spent £1,500 on a graphics card to end up with constant issues with it. It lets down the rest of the machine which is an absolute beast. Disappointing that spending so much money results in such shoddy quality control.