The rings were most likely both for ranging purposes.
The Mk.VIII sight was calibrated so that a target with a 30ft wingspan would fill the inner 50mil ring at a range of 200yds, and the outer 100mil ring at 100yds (by extension, an aircraft with a 60ft wingspan would fill these rings at 400 and 200yds, respectively).
I THINK this formula is correct for how it works:
(Distance in yards) = 1000 / 3 x (Object size in feet) / Mils
I tested it with both the 30ft and 60ft wingspans and it seems to hold up.
So consider the G4M with a wingspan of 80 ft. If you plug this size into the formula, the Betty would fill the 50mil ring at a range of ~533yds and the outer ring at ~266yds. The Zero with its 39ft wingspan would fill the two rings at 260 and 130yds, respectively.
The hash marks inside and below the rings (extending out to 150mil) are in 5mil increments. If you can estimate the target's range, speed, deflection angle, and flight time of your bullets, you could then use these hashes to determine how much lead you needed to give the target when shooting. The rings can help provide a quick visual shortcut for this rather than counting hash marks: You KNOW the 50mil ring has a radius of 25mil, so if you need to give the target 30mil of lead it would automatically follow to line the target up with the first hash below the 50mil ring (with the ring being at 25mil lead).
Once I can figure out what the formula is (I'm trying to find it. That's proving more difficult than the range calculation one) I'll work on putting up a lead chart for the Mk.VIII sight at various ranges and airspeeds.