Not sure if you mean Windows restarted, or if the system actually powers off and you need to press the power button to turn it on again, but in my opinion, usually only hardware problems can cause the system to power off completely although the combination of hardware and software problems might be causing this for your particular unit.
Anyway, still think the system should never power off unexpectedly if the hardware is working right, so would still consider it even though it doesn't appear obvious.

There probably isn't a whole lot you could do for hardware issues, but some ideas are below.
Yes, would still really like to hear if anybody else with the same model has tried the same things to get a better idea of the situation

1. Remove extra memory or try other memory.

2. Compare on battery and AC power if you haven't already to check if there is any difference.

3. Try more games if there have not been many tried.

4. Check and tell us your temperatures anyway, just to make sure they don't sound too high.

5. You probably don't want to try this right away, but if you have a spare hard drive and can, try a clean Windows installation with drivers from just the ASUS download site for your model before you start updating any drivers.

6. Doubt it is possible, but if you know somebody else with the same unit (maybe a local store?), check theirs too.

7. If you're still under warranty, consider sending it to ASUS to check while you are still covered, but might not be easy or fast for ASUS repair to catch unless your hard drive can be moved to another G75VW unit to compare with (back up your data first and allow them to erase your hard drive if necessary?).

Well, hopefully we can hear from others who have tried it or have better ideas.