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I think you're seeing milliradians - a radian being a circle divided by 2*PI, which is mathamatically convenient. PI is obviously 3.1415..., so 2*PI = 6.283... - or round it up to 6.4. Then divide each radian 1000 and you get 6400 units to make a full circle. Normally only the first two digits are marked on a compass.

However, Mills were dreamt up by Charles-Marc Dapples in Switzerland in about 1850 - you can't blame the US military for this one! Continental Europe was messing around with degrees and metrication (hence the Gradian, 400 to a circle and 100 to a right angle). A milliradian (or Mill) does actually have its uses. Because it's defined from the radian, it's fairly easy to calculate using the angle of the arc of an observed object and it's distance. If an object in the distance is 5 Mills from end to end and you know it's 1000m away then you know it must be 5m wide (don't forget it's 1/1000 of a radian). I'm using metres, but the unit obviously doesn't matter as long as you use the same for both measurements. This works backwards - if you know the size of an object (such as a tank) you can easily work out how far away it is - of great interst to the military, which is why the Mill has found favour with the artillary.

Sorry to contradict again, but the Grad wasn't developed by the British millitary - the French are responsibe for that! It was used in various European countries as the "metric degree" for a while (and might still be in some odd places for all I know). Living in England all my life, the first time I came across a gradian was as a weird button on a scientific calculator in the 1970s. I don't belive I've ever come across it in the millitary; I could be wrong but it's most likely to be Mills or degrees. I believe that the French millitary do use(d) gradians, for all the good it's ever done.