Power from the driver = Power consumed by the LED
0.85 is 85%, which is a moderately high, but still reasonable, driver efficiency value.
7.4V is the nominal voltage for two Li-ions in series.
3A is the advertised drive current.
3.35V is the datasheet value for the XM-L's forward voltage (Vf) at 3A drive current (If).
Driver power sent to the LED is driver efficiency*Vbatt*Ibatt.
LED power consumed is Vf*If.
Thus, 0.85*7.4*Ibatt = 3.35V*3A. Solving for Ibatt gives you 1.6A.
People measure tail current probably because 1) it is easy to do, 2) it suggests what sort of run time they might get, and 3) it gives them an idea as to how hard the cells are being driven.
Measuring drive current at the LED requires access to the LED, which is not always possible (the head may be threadlocked and thus sealed). You have to measure the current in series with the LED, which generally requires that you de-solder the connection to hook your DMM into the circuit. That can be a hassle. If you screw up your connections with a boost driver and feed it an open load, you often will kill the driver.
I have no idea what DX's advertising copy is supposed to mean. All I can do is assume that the 3A refers to drive current.
To estimate lumens from drive current, refer to the LED's datasheet. There is typically a graph of relative luminous flux vs drive current. Find the value of relative luminous flux for the drive current of interest and apply that RLF factor appropriately. For the XM-L, at 3A, RLF ~325%. Multiply that by the lumens at the standard forward current. For the XM-L, you can see from the graph that this current is 700mA (that's where RLF is 100%). You also can infer this from the fact that the lumens rating for a T6 XM-L is given as 280 lumens at 700mA forward current.
280 lumens * 325% = 910 lumens. This is the estimated lumens at the emitter. You will have losses from the reflector or optics, the glass window, LED junction heating, blockage by the bezel, etc. Multiply the emitter lumens estimate by say 1/2 or 2/3 or 3/4 or whatever to get an estimate of the out the front lumens.