-I understand idle temps, there may be little difference between air and liquid, but which one can maintain a cooler temp when gaming for 6+ hours?
Either, it really just depends on your ambient room temps, case airflow and choice of cooler.
-Aesthetics; if I have a window on my tower, does closed loop look sleeker and better maintained?
This is a matter of preference for most people, so you would need to determine this
-Dust; will there be less dust build-up with liquid cooling?
This depends, you can also have dust buildup with normal air coolers as well. Anytime a fan is moving air, dust has the ability to accumulate
-Risk; what are the chances of a closed-loop springing a leak or drying out?
Ideally never. They are designed to be sealed, hence the term 'closed-loop'. If you develop a leak, you should immediately contact the manufacturer for an RMA replacement. If you have a custom loop, all of these factors are based upon how well you assemble the loop...if you take your time and do it right, you shouldn't have any issues.
-If I am not overclocking the CPU or GPU, is there any reason to even have extra cooling?
Most people will tell you no. I have my CPU and GPUs at stock for now, but I watercool all 3. I do it mostly as a hobby and for fun, but it's something that differs from person to person. You can overclock CPUs and GPUs without using watercooling and using normal air coolers.