Laser ablation.
Once the laser hits something it transfers energy so powerfully that parts of the target turn into plasma. The lasers will then instead hit this plasma and excite it further, turning it into an explosion which in turn propels the target further away from the laser.
For math on the topic I direct you to the end of this informative page by Randall Munroe:
https://what-if.xkcd.com/13/
So, this can happen, although it depends on the intensity of the laser, the wavelength of the laser, the length of the pulse, and the surface of interaction. In general, the equation to determine the momentum (p) of a photon, given the energy (E) is p=E/c where c is the speed of light. The energy of a photon is given by E=h*c/λ, where λ is the wavelength of the laser. Assuming that the laser is 700 nm red (although any visible light will be different by less than an order of magnitude) this means that the energy per photon will be 2.84*10^-19 J, resulting in a momentum per photon of 9.48*10^-28 kg*m/s. This is small.
Next, we need to know how many photons are being emitted. Damage thresholds for many materials such as metals are in the kilowatt or higher range. As this laser is able to cut through armor, a few hundred kilowatts of continuous power seems a good start. Let's assume that Triumph will show the laser to fire for much more than a few microseconds, making it close enough to continuous for our needs. 100 kW of power means a lot of photons. To make the math simple, let's use 1 second as the time of the shot, resulting in an energy per shot of 100 kJ. This yields 3.5*10^23 photons per shot, and 3.34*10^-4 kg*m/s of momentum. This is not a lot of momentum.
If you want an appreciable momentum transfer, then the target needs to reflect almost all of the light, doubling the momentum transferred per photon and allowing for much higher damage lasers to be used. If the average target has a mass of 200 kg and needs to move 10 meters to get to the next space (I'm pulling numbers out of this air here) and will be slowed by friction, this would require at least 8*10^6 kg*m/s of momentum transfer, assuming that gravity is approximately that of Earth. Which means a shot providing 1.2*10^15 J. This is a lot of energy. That is 6,000,000 lightning bolts simultaneously. This is not the energy that the target receives (remember, it is now perfectly reflecting) but rather the energy produced by the laser. So, this seems unreasonable. The light produced by this would definitely blind everyone on the battlefield, get absorbed somewhere else (the bike itself is the most probable) vaporizing that target, and would likely blind everyone on the planet.
All of this becomes more complicated, however, if the target receives any damage at all. This is when the point about laser ablation comes into play. The write-up done by Randall Munroe is excellent (and hilarious) but seems to imply (to most laymen) that the target would necessarily be destroyed before it moved. This is not the case. Here is where I stop using math to explain. Having worked with ultra-short pulse lasers for a number of years, I have seen them shot at many things. My favorite is watching the interaction with Jell-o. Our ultra-short pulse laser produced about 1 millijoule of energy per shot, and was enough to make the jello wiggle. This is due to the plasma that it generates upon impact with both the Jell-o and the air. The target was less than a square millimeter, but was able to make a liter of Jell-o wiggle. The reason for this is that the energy was compressed in time down to 70 femtoseconds, or 70*10^-15 seconds. This gives a peak power of about 14 gigawatts. It is this enormous power, rather than the energy of the laser, which enables this sort of plasma generation
Jell-o wiggling is a far cry from a person in a suit of armor being pushed backwards, but the point is made clearly enough. The jell-o was still almost entirely intact after the laser. Much of the momentum transfer came from the plasma in the air, not the Jell-o. The point of this huge wall of text, which, admittedly is likely awful to read, is that if Triumph wants an explanation of the ability to push an object backwards via laser light, they should insist that it be a short pulse (just for animation purposes, as our eyes would still be able to see the after-image of the laser, this should last for just a few of frames, not even a second) and make sure to animate a purple (oxygen glows purple when ionized) glow around the point where the beam hits the target, due to the color of the plasma.
Also, don't ask how shields would interact with this because I do not know how they would physically work.
TL;DR Yes, this would work, even without destroying the unit, but could use an animation implying short plasma bursts.