Here's my 2 pennies.
"...this application requires a ground rod?" No, I see the refer box, assuming it is a shipping container or the like, as equipment. Not a structure, or intended to be used as a shelter of any kind. Grounded yes, rod/electrode no.
"...this ground rod is acceptable?" Heh, Heh... No! If it were the sole ground, it would be useless. ( I have seen rods this short used in antenna applications. 3-6 in a pattern around it. No idea what purpose they serve in that way, but...)
"...does the white need to be re-identified as it is used as an ungrounded conductor?" No. 200.7C(3)as mentioned earlier.
