The magazine of Frostfire is placed in a position that "seems to hinder" the sight during aiming, but the image displayed on the lower right seems to tell us...the proper aiming of Frostfire is aiming by "over looking the magazine itself", this is indeed a very cool concept. From the lower right image, I presume the Frostfire is a close-range energy-carbine...shall this be true, a perfect aiming system well indeed not of a need when damage plays more of an importance in close-range.
It would depend on the mass. Force = mass * acceleration. The acceleration is large (assuming like a bullet) but if the mass of the plasma is less than that of the bullet, there will be less recoil. I'm not sure how the gun works. If it uses the Hall Effect, then there will be some recoil. If it is just throwing electric charges out to generate plasma, then it will have no recoil but will be crazy dangerous (like electric plasma everywhere)
If it fires ionized gas using the Hall effect, then it will have a sustained and targeted arc, but the spray of gas would weigh some amount (from what is shown, it must be at least 2 grams though probably closer to 10) so it would have the recoil of a paintball gun (think of the compressed air in a paintball gun being the primary mode of fire rather than the actual ball. Even without the ball, the force is the same).
If it fires electrons ad-hoc, then it would be, more-or-less, a bolt of electricity and would have 0 recoil. The effect is the same as a laser, electrons aren't being propelled as much as they are just transferring their energy to adjacent electrons resulting in the ionizing of the air around it (very little mass, very little acceleration = practically zero force).
From the look of the weapon's concentrated fire though, either it is the former mechanism or the target is made of metal in a room full of plastic