Wikipedia: "The word aurochs was borrowed from early modern German, replacing archaic urochs, also from an earlier form of German." So it's the same "Ur-" bit.
In Swedish, it's still "Uroxe".
Although it seems that this interpretation of the "ur-" part might have been retroactively fitted to mean ancient, primal. Etymology Online says:
"from German Aurochs, from Old High German urohso, from uro "aurochs" (cognate with Old English ur, Old Norse ürr), which is of unknown origin, + ohso "ox" (see ox). Latin urus and Greek ouros are Germanic loan-words."