The video isn't really clear enough to tell. Larry's advice is okay on this topic (but not his spelling, even that's blinded by his "rightness" or his penchant for homophones). The big fan in front of the compressor better replicates on-the-road conditions so your gauge readings are more accurate. If you have a shop do it, they should also do this, particularly if the ambient temps are high.
If you're going to check it yourself and it's R-134a you can pick up a low priced gauge set from Harbor Freight. READ THE INSTRUCTIONS AND WARNINGS!
On your model car the fans and the compressor share some switch gear so the low speed fans and the compressor cycling are probably related. M-B modified the designs from year to year, so you'd need to review the wiring diagrams in the EPC Startek site to verify their operation regarding turn on at low-/medium- pressures and temps. I'd recommend reviewing the FSM before doing any work on an unfamiliar system as a matter of course.
Maybe you're low on refrigerant and the pressure switch cut out the compressor, which also cuts out the fans, or maybe there's something else that's triggering the cycling.
With a functioning unmodified system the built-in safety features should protect the system from damage. If the pressure goes too high, a safety switch will cut off the compressor; if it's too low, likewise. If it ices over, it'll cut off. But if there's persistent cycling you could have increased wear on the compressor clutch. Minor, but possible, although I wouldn't characterize that as 'damaging the system.'
If/when you get numbers from a gauge set, I recommend this site for comparison:
http://www.ackits.com/aacf/ptchart.cfm Notice that you can have a relatively wide range and still be "normal" in a -134a system.