To convert this into a human-readable date and time, open a terminal and do this:
python
>>> import time
>>> time.strftime("%a, %d %b %Y %H:%M:%S", time.localtime(1474441704.265237))
You'll get something like 'Wed, 21 Sep 2016 07:08:24'(I'm sure you can do this in other languages than python...)
date -r 1474441704If I understood correctly, this particular bug was only exploitable from the GUI and this machine hasn't been away from home, so it's likely this isn't related, but posting here, in case it's part of a bigger picture.
Did you also have sshd running, and do you know what kind of network you were using at the time?