It's not adding so much as averaging. You have a 1:1 voltage divider there, so the open-circuit voltage at "MONO SUM +" will be halfway between the voltages of the two channels.
But why resistors, and why those values? Well, your audio device is capable of a certain amount of current. It expects to be driving headphones or speakers or whatever. If you connect the two channels directly together, then whenever their voltages are different (which is most of the time) they will be trying to pull each other up or down, with absolutely as much current as they're capable of. This isn't good for longevity, or battery life, or audio quality. With 2k of resistance between one channel and the other, the amount of current that they can use to fight each other is limited to around 1mA or less, which is probably fine.
But there is a down side, which is that this circuit is only really suitable for driving a high-impdance load (like the inputs of most amplifiers). The output voltage is the average of the two inputs when the current flowing out through MONO SUM + is pretty close to zero. But if you connect it to a load with an impedance of less than a few thousand ohms (say some 8-ohm speakers) then the voltage at the output will be much lower, most of the power will go into heating those two 1k resistors, and very little of it will go into the load. Again, the resistors make things safe so that you won't actually kill your audio device, but the result will be a low audio level.