Would playing World of Warcraft on a laptop for hours at a time
stress the hard drive? I ask because my daughters hard drive started struggling since she started playing the game, and now it is toast, and needs replaced.
A hard-drive will go when it has to go. Playing WoW isn't stressful enough to cause failure as the game is initially loaded off the HD and placed mostly into RAM.
Heavy video-editing/etc would put more stress because of the constant read/write going on, but again Hard-Drives are meant to be used like that, if it failed it could have been a number of things like age, defective etc. If its only a few years old you could call the manufacturer and have it RMA'd under warranty. Usually HDD warranties are between 3-5 years.
Depends how much RAM you have, how hot your laptop gets on the inside, and where it's being used.
For example: If you have very little RAM, the hard drive is going to be churning constantly. If, on top of that, your laptop generates a lot of heat and is used on a soft surface in a hot room, the heat will make things worse for the hard drive and it will fail.
On the other hand, if you have a very well cooled and energy efficient laptop with lots of RAM, it'll be fine for a good long time.
IMO the vibration from games usage if using the laptop's keyboard could be a cause, but not the HD access pattern.
Of course, extended gaming increase heat and HD's life goes into toilet when you start going above 45C and none in the consumer market is designed for above 60C for extended usage.