Criteria for gyroscope export restrictions
From the Bureau of Industry and Security:


  Section 742.6 of the EAR requires a license for RS reasons to export
  certain image-intensifier tubes, infrared focal plane arrays, certain
  software and technology for inertial navigation systems,
  gyroscopes and accelerometers, to all destinations except Canada. All license applications for these items are reviewed on a
  case-by-case basis to determine whether the export could contribute,
  directly or indirectly, to a country’s military capabilities in a
  manner that would destabilize or alter a region’s military balance
  contrary to U.S. foreign policy interests.


(emphasis mine)

Basically, it's a pretty good gyroscope. In theory, you could use this to make a weapon that is as good as or better than something that we have. So of course we can't let you have it.

As mentioned above, "these items are reviewed on a case-by-case basis". So there are no published criteria that I could find.

But a quick search on Mouser showed that there are a couple with a "EAR" tag in the description indicating export controlled. But there are plenty that don't have this tag. Such as the A3G4250D which seems to have very similar specs to the L3GD20.