I’d say about 99% of the software I install through BigFix is done system wide using the SYSTEM account. Installing per-user applications as the current user is difficult because you have to do this for every user that logs into the system at least once, but you can’t do it until they log in.
It could be the case that Office 2016 is a per-user install, but I’m fairly certain Office 2013 is not. I’m guessing there was something else wrong with what you attempted.
This could be related: Office 365 installation completed but action returns exit code :17002 or 17004