I don't see how you can possibly trademark a year, which is a factual statement.
Also, I think it really clashes with the supposed spirit of the games. If it is not a friendly, peaceful and international battle of athletes, but just another event where McDonald's and Samsung can advertise without any distractions, why do we need it? And why should a city finance it?
To be fair, Cadbury has trademarked a specific tint of paint that they created (which is the important bit). It just looks surprisingly like purple to the rest of us. ;)