My physics is a little rusty...
Do magnetized ions have mass? If so, then would that require this device to be anchored on a large mass, like a planet/moon/etc or have some sort of opposite force to keep the device in place in space as the ions spew out?
Sure they have mass. The article says the beam would come from a station in space. I suppose they've done the math.
Yes, magnetized ions would have mass. However, if the craft simply dumped ions in two directions symetrically at the same time, its orbit would be unaffected as far as I know.
Kind of like if you were in a two person kayak with one person rowing backwards. There'd be lots of motion, and lots of water moved around, but you wouldn't get anywhere.
My guess is the plasma station has two ion guns. One shoots at the sail. The other shoots opposite. Ions hit the sail, propelling the ship. The use of a second gun prevents the station from recoiling, although more energy has to be used for the second gun than the first to compensate for rebounding ions from the sail striking the station.