This question is testing COMPARISONS. We must make sure that we are comparing "apples to apples."

Ranked as one of the most important of Europe's young playwrights, Franz Xaver Kroetz has written forty plays; his works - translated into over thirty languages - are produced more often than any contemporary German dramatist.

If we strip away the modifiers, here is the core comparison:
his works are produced more often than any dramatist.

We're comparing WORKS to PEOPLE. A correct comparison would either compare WORKS to WORKS or PEOPLE to PEOPLE. Since "his works... are produced" is not underlined, we can't change that part. So we must change the second part to compare his works to other works.

(A) than any
Compares works to people. Incorrect.

(B) than any other
Still compares works to people. Incorrect.

(C) than are any
Still compares works to people. Adding the verb "are" doesn't fix this. Incorrect.

(D) than those of any other
"Those of" stands in for "the works of other dramatists." Correct!

(E) as are those of any
The idiom "more often" requires "than." We cannot use "as" in this comparison. Incorrect.

The answer is D.

Nota bene: there is a meaning difference between "more than any X" v. "more than any other X." For example:
1. Alaska is bigger than any US state.
v.
2. Alaska is bigger than any other US state.

The 2nd sentence is the correct one. "Any" implies that Alaska is outside of the group "US states," and is bigger than any member in that group. "Any other" implies that Alaska is in the group "US states." Since we know that Alaska is a US state, the meaning of the 2nd sentence is the correct one.

HOWEVER - this is something that the GMAT is very unlikely to test you on! In the Kroetz sentence,
his works are produced more often than those of any contemporary German dramatist. => Kroetz is NOT a German dramatist.
his works are produced more often than those of any other contemporary German dramatist. => Kroetz IS a German dramatist.

The GMAT could hardly expect a test taker to know whether this guy is German. (His name sounds German, but he could be Austrian, Swiss, etc). Since the meaning difference relies on outside knowledge that you couldn't be expected to have, this was just a red herring.