Unable to update third-party apps on macOS Sierra -- temp dir not writeable
This indicates that the permissions on that folder have become corrupted, or were changed by some other process.  My suggestion would be to follow the directions in the link below, and reinstall Sierra from the Recovery Partition.  Doing so, should reset the permissions on that folder, which should then allow you to successfully run the installer.  Just make sure to pay attention to the part where they say, "Skip Step 2 because you will not be erasing your disk.".

https://discussions.apple.com/thread/7715561?start=0&amp;tstart=0