The "equations and maths" may be good (I didn't look that closely), but I don't think it's proper to equate the kinetic energy of a bullet with the energy of a burst of light and then figure out the recoil of "something going at lightspeed."
Yes, photons have something that acts like mass (insert "I didn't know they were Catholic" joke here) or momentum, as can be demonstrated with a lightsail, but it's very low and I'd think insignificant for a hand-held laser, unless it's so powerful the beam causes the air it shoots through to heat up so fast it burns and explodes, in which case it's got worse dangers than a little recoil.
I'm not sure how to calculate the recoil, but I'm confident the method used is wrong. It assumes some small mass is accelerated to lightspeed, but it would actually take infinite force to do that. I'm not sure if the Lorenz transforms would be used here, or something else. I think I'd go to Wikipedia and look up lightsail and photon pressure (for the frequency of light the alleged laser pistol puts out), and calculate it from the pulse power (how many photons get emitted in a firing of the laser gun). This, as best as I can figure (by just thinking about it a minute), is unrelated to the kinetic energy of a bullet.
Again, the laser gun WOULD have some small recoil, as the light comes out one end, and nothing out the other (in a "lasing" medium, light goes all directions, but gets amplified most along the longest dimension, and for pulse lasers there's usually a mirror at one end to make it all go out the other end, so it's going to push on the mirror just as it does on a lightsail), but not all "guns" have recoil. A bazooka is essentially a rocket launcher with a hole out the back, and all the expanding gases go out the back instead of building up in the barrel, so a bazooka has no recoil.
As for the extremely short time of the recoil force, I don't think that's a "problem." A gun's recoil starts when the bullet is fired, then pretty much ends as it comes out of the barrel, and that happens in what, maybe a millisecond or two? It causes the gun to have a backward speed, and that pushes back on the hand or shoulder, depending on it being a pistol or rifle. The same recoil from a 30 nanosecond laser pulse wouldn't be noticably different from a 1 millisecond bullet shot. As far as human perception, the gun is suddenly, instantly moving backwards at a certain speed.