Dalv is right that you would ideally bring the mic closer to the source you want to record, although that isn't technically what signal-to-noise means. Good mic placement is going to have the most advantageous effects for your situation. Also, that mic has a cardioid polar pattern which means that it picks up in a spherical orientation around the front and a little around the sides and back relative to the condenser element. You'll want to place it such that the unwanted noise is as far behind the mic's screen as possible. If you sit at a desk, keep your hands under it while you play, and make sure that the mic is facing away from your hands. Sometimes side address condensers like that capture quite a bit of signal behind them because the whole back of the element is open, so you could even try a gooseneck isolation shield on your stand set up behind the mic to block unwanted noise.
In addition to this, try turning the audio settings of your games all the way up, if not already, so that the game sounds will be more likely to drown out the clicks from the controller when you are not speaking. If this means you have to increase the gain on the mic, then it may just defeat the purpose, because the clicks will get louder, too. But finding the right balance could help a lot.
You don't mention if you are editing after recording, but, as that is a USB mic, it'll likely be your only option for adding audio effects (i.e. you can't plug it in to outboard gear). Simon's suggestion of a noise gate is spot on. It is a kind of effect that will only allow sounds above a set threshold (volume in dB) through. It ought to be very easy to set the right parameters in your case, as I presume your voice will be many decibels louder than the clicking. Lets say you see the wave file and you can watch your voice averaging at around -5db. You could then set the noise gate effect threshold to -15db and likely eliminate the noise while you are not speaking. Keep in mind that background noises will be audible while you talk - noise gating is an "all or nothing" deal.