The Great Beethoven fallacy, based on the referred article, is that, if we kill a fetus, we are killing a genius who will come to be in the future. You ask what kind of fallacy would subsume the Beethoven fallacy. I offer the counterfactual fallacy as an answer. That is, the Beethoven fallacy is a counterfactual fallacy applied to a pro-life argument.
The counterfactual fallacy occurs when one treats a hypothetical (or counterfactual) situation as if it is a fact, and then draws a conclusion about the future or the past based on the counterfactual situation, but the evidence for the conclusion is almost none. Of course, not all counterfactual inferences are fallacious, as is shown in the following case: "If this coin had not landed on the head side, it would have landed on the tail side." This counterfactual inference is not fallacious because of the well established fact that a coin toss results in a binary case (assuming that the coin is unbiased and landing on the side is impossible).
An appeal to a counterfactual situation commits a fallacy if it lacks well established facts relating to the situation. The circumstance of the pregnant woman in the above case is such that the probability is almost zero that the future person will become a Beethoven. The apple never falls far from the tree! It is more likely than not that, had the fetus been born, it would have lived an unfulfilling life. This is why the pro-life argument based on conterfactual situation is fallacious.