Old buildings (pre 1968) in the USA can have un-earthed wiring 'grandfathered' in and it is even code compliant to replace a 2 pin socket with no ground to the wall box with a three pin one. However *EVERY* such socket *MUST* be marked "NO EQUIPMENT GROUND"

http://ecmweb.com/code-basics/article-406-receptacles
As such, your best course of action is to stop using that socket and go to the hardware store and get a neon socket tester that will indicate whether or not a socket has a ground, and also detect miswiring. If only a few sockets are missing their ground its probably a real wiring problem that your landlord will be obliged to get fixed, but if a lot of the sockets are ungrounded, and its an old building so that the circuit was originally legal to install without ground then its possible that all you may get is the code required warning label affixed to each socket, and if you actually require a grounded circuit it will be at your expense
You focused on the labeling requirement and skipped over the far more important GFCI requirement! Even though your picture and link explain it correctly. Without the GFCI protection, it's only LEGAL to replace a worn-out 2-prong outlet with another 2-prong outlet on existing installations.
That said, it's common to find ungrounded 3-prong outlets installed in older 2-wire systems without any labeling, usually by someone who lived in the place at the time and were tired of dealing with 3-prong adapters. Doesn't make it code compliant, but it is a cheap practical solution.
So to the original poster, yes you may have an issue with the landlord if you want to raise it, and depending on whether its one outlet or all of them.
The landlord can say no, at which point you can contact the local authority with the power to inspect and force code compliance. This all takes time. One possible outcome is for the landlord to replace all the three-prong outlets in your place with two-prong ones, which brings it back into compliance with the original code it was built under. Which probably won't make you happy...