The simple answer is logistics.

The Kalmyk Steppe was a pretty rough place in 1942. From the Volga River southward, there wasn't much in the way of east-west infrastructure. The railroad ended at Elista, at the far western edge of the steppe. A rude road connected Elista to Astrakhan across the steppe.

As Army Group B became invested in the Battle for Stalingrad, Hitler saw the same map that you did (well, something like it, at least) and became alarmed at the possibility that the Soviets might be planning a counteroffensive from that area. According to the U.S. Army's official history, Moscow to Stalingrad, Hitler ordered the 16th Motorized Division to go to Elista. So short was the fuel situation for the Germans that Gen. Kleist, the army's commander, had to drain the tanks of a panzer division to get it into place at the end of August.

The division wasn't entirely alone ─ it had the support of many Kalmyk cavalrymen, who kept up with the division's armored cars with their horses. Essentially a "free corps" of cavalry, the Kalmyks were a motley crew who used captured Soviet weapons and fought alongside the Germans.

In the first half of September, the 16th division sent out a famous patrol whose activities are charted in a story within Paul Carell's Stalingrad: The Defeat of the German 6th Army. I don't like using Carell's stuff because there's many better books out there, and he has a nasty tendency to leave you guessing about where his information is coming from and whether it's reliable.

That said, the account reprinted here from his book describes how a patrol from the 16th penetrated to within 20 miles of Astrakhan before being turned away by Soviet defenders dug in along the Volga. The patrol also destroyed an oil train that was traveling the narrow, hastily built rail line between Baku and Astrakhan.

Before retreating, the patrol became the German unit to reach the farthest east in all of Barbarossa.