Why doesn't the winding coil burn
Ignoring the effect on the waveforms of motor winding inductance (Which you really cannot do, but ignoring it makes the math much less messy).

If we assume a standard three phase machine which at any given point has one winding directly across the supply and two windings effectively in series also across the supply, then for 200A of DC input one winding sees  133A and the other two see 67A each, further the 133A winding is only conducting for 1/3rd of each cycle while conducting 67A for the other 2/3rds of a cycle.

If these waveforms were square (which they are NOT), you would get average (Per winding):

((133^2)/3 + (67^2)*2/3) * 0.006  = 54W (IRMS = 94A) for a total copper loss of ~162W distributed across the three phases. 

Assuming a motor Tcase of say 100 degrees C, and winding temperatures of say 200C (220C magnet wire is an off the shelf thing), then you can tolerate nearly 1.8degrees C per watt between the winding and the case, which should not be a showstopper (This ignores the heat from the iron losses which is likely significant). 

Of course you still have to get rid of the 162W from the motor housing without letting its case get too hot (Big low speed machines often have auxiliary blowers to handle this). 

While I have my doubts that that machine actually meets that spec, it is not completely impossible at first glance.