<The radio waves can exert force upon an object that they hit, but they don't have any mass to push the emitter in the opposite direction. Is this what you two are saying?

Basically, yes. An electromagnetic emission, like shining a flashlight out the back of the rocket, does create thrust on its own, but at feasible power levels this is so small as to be almost useless. Of course, if you have enormous amounts of power available, and the means to convert this to a light beam and control it (i.e. keep it from melting your ship), then you have the classic photon rocket. This is not feasible using current technology.

If it is, then couldn't you put the radio emitter on the front of the spacecraft and let the radio waves hit some sort of sail to pull the ship along?

This is the classic "why can't you put a big fan on the back of a sailboat to make it go" question. If both the emitter and the object it acts against are attached to each other, there is no actual thrust generated since the net mass of the system is still the same, i.e. nothing is being thrown "away." Now, if your emitter is located somewhere else besides the ship, like on the surface of the Moon, then this could work, in the same way as Bob Forward's laser driven solar sails.

I just don't understand how the radio waves can have the mass to push an object they come into contact with, but not enough mass to be used as reaction mass.

This is a good question, especially in a vacuum, but I don't have the information from the article or the physics background to answer it.