I know that the answer is yes, I should, but outlets near the setup are not grounded (even though they look like they are) and I don’t want to have wires running though my living room.
The real question is what are potential problems ? Occasional system reboots? Permanent damage to PSU? Permanent damage to other components?
Generally speaking most buildings can be “grandfathered in” under code such that it’s perfectly legal to rent as long as the electrical system functions and meets code for the year on which it was built or installed… shitty, but legal.