After using a 3/8 square drive, I found a Snap-On tool (socket bit) that specifically called out usage for Cummins oil drain plugs. I'm a sucker for special tools so I got it. It's a 10mm square drive so it fits a bit tighter and I feel better about not rounding out the drain plug. My opinion, either should work, but I would use the "squarest" 3/8 drive you you can find. Some ratchets and extensions have very rounded shapes to make getting sockets on and off easier. More likely to dent the square hole in the softer drain plug, though.
I agree with B. G. , it looks odd because the broach shavings are pressed into the bottom of the hole and it looks like a torx or something.