I always dry mine in the dryer unless I am touring and the dryer isn't an option. I don't think it has shortened their life at all. I have some that are 20 years old and have had thousands of washings. Yes they are pretty much shot, but at their age I think that is to be expected. The fact that they are still around says that they hold up to the dryer just fine.
I think Machka's comment about the dryer fluffing the chamois is valid too.
I wear fairly inexpensive shorts (Performance Century or similar). I assume that more expensive ones should hold up as well or better to the dryer, but maybe not.
If in doubt follow the recommendations on the care label.