We eat rice quite commonly in Germany and not only for asian dishes. It has been cultivated in the meditaranean for at least 1000 years. But sure, Bread, noodles and Potatoes are much more common (Even though potatoes being south american, are only around for 350 years). Still the Kochgeschirr would not be used that way outside of emergency situations. It's mainly used to receive food from a field kitchen or to heat up MREs (There is an asian themed one with rice :P ) on a metal fold dry fuel stove.
We had similar ones during my service in Germany a decade ago. Even though I can't say with confidence whether or not it was exactly this one. The main purpose of it was to get handed out the food into it from a field kitchen. If you stick the inlay into the one handle and grab the big pot by the handle too, you can fit all three pieces in one hand. We also used it to heat up MREs on a little dry fuel fold metal stove (google "esbitkocher"), which also already was around during WWII. I would think it was no different in WWII. Maybe it was delivered by a notifier from the field kitchen further back.