The first clip in the following video shows a Falcon 900X performing a low pass:
What exactly is considered reckless here and why would the pilot lose his license?
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This event appears to have taken place in Argentina. However, I cannot determine if it is a civil aircraft of U.S. registry ("N" numbered aircraft).
If it is not a civil aircraft of U.S. registry and took place in Argentina then the applicable U.S. regulations (14 CFR Part 91) would not apply.
However, if the aircraft was a civil aircraft of U.S. registry operating in Argentina then, according to 14 CFR 91.703 (a) (3) most of 14 CFR Part 91 would apply, "...so far as it is not inconsistent with applicable regulations of the foreign country where the aircraft is operated or Annex 2 of the Convention on International Civil Aviation."
If 14 CFR Part 91 does apply, the regulations and policy shown below would likely be applied regarding the pilot(s), assuming the FAA was made aware of the issue.
14 CFR 91.119 (c) - Minimum safe altitudes requires that an aircraft remain at least 500 feet AGL (or no closer than 500 feet to any person, vessel, vehicle, or structure in sparsely populated areas).
Also, as noted in FAA Order 2150.3C - FAA Compliance and Enforcement Program on page 9-3 (near the bottom of the page) "Reckless" is defined as:
Reckless. A violation is reckless when the violator's conduct demonstrates a gross disregard for or deliberate indifference to safety or or a safety standard.
(a) Aircraft operations for the purpose of air navigation. No person may operate an aircraft in a careless or reckless manner so as to endanger the life or property of another.
Also, on page 9-22 of the FAA Order 2150.3C (see the image below) note that even over an uncongested area low flying is considered as a "Severity 2" violation (with Severity 3 being the most severe).
So, if the pilot's license was revoked it probably was due to the regulations and policies noted above.
(During airshows where aircraft are flying/operating lower than FAR 91.119 - Minimum Safe Altitudes would allow, an FAA Waiver is written that contains provisions and restrictions that provide for an equivalent level of safety)