I wonder if the directions are generic and refer to tradional cast iron as well as those pieces that are enamel coated. I agree with you, from this picture and the write up I would think it is traditional cast iron.
I sometimes add a little water, as though deglazing, and leave the pan on the stove, but off the heat, until I am ready to wash. It prevents food from drying, making it easier to wash and I have never noticed it doing any harm.
I have used cast iron my entire cooking life and I will be 66 this summer. If you ever see any rust, wash with warm soapy water, dry, and rub a little cooking oil onto the surface and then heat and wipe out any excess oil. Should be good to go. You might also consider lining the pan with a paper towel or coffee filter if you are going to stact something else on top of it. I'm sure you will enjoy your griddle for many uears to come.