I donwloaded the installer, but when I tell it to install, it gives me an error. It says that it requires an older version of wow.exe to install so it will not install. That doesn't make any sense to me. How am I supposed to fix this? Obviously I can't downgrade to the older version of WoW, and I don't see why they wouldn't let you play just because you have a newer version.

First thing's first: try Blizzard's Repair Tool (it should be in your WoW folder)

If not:
most likely cause: your WoW install is infected with malware or is corrupt.

1. Uninstall the PTR-version, delete the folder and try reinstalling it.

If this doesn't work

2. Use an antivirus software (I used Malwarebytes for example but there are many others)

If you still got some active malware running on your PC and the antivirus software can't handle it, you should simply reinstall your operating system (you might also want to format the partition you had the WoW install folder on)