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I was surprised to discover my dictionary had this entry for dilemma:

a situation in which a difficult choice has to be made between two or more alternatives, esp. equally undesirable ones

The notion of dilemma meaning two or more flies against what I was taught about the word. The very idea of a false dilemma is specifically based on the number two.

Has my dictionary merely updated its definition to encapsulate the many people who use dilemma for more than two equal choices? Or was someone in my youth being unnecessarily pedantic?

The etymology for dilemma reveals that the original meaning of the word was specific to two (di-) premises (lemmas). In fact, Etymology Online states

It should be used only of situations where someone is forced to choose between two alternatives, both unfavorable to him.

So yes, it should properly only be used for two unpleasant alternatives. I would speculate that your dictionary has been updated to include more modern usage, which is less specific about the number of choices to be made, perhaps because the "important" part of the meaning is that a person must make an unpleasant choice.

Interesting - I first encountered the expression false dichotomy which I think expresses the intent more accurately despite being slightly pompous. I was then mildly surprised to find the term more popularly written and spoken as dilemma since as you point out a dilemma is not necessarily and certainly not intrinsically limited to two options.

I also prefer dichotomy since by definition it suggests a division into two non-overlapping or mutually exclusive parts, and since conflicting opinions are almost never mutually exclusive - the possibility of mediation presupposes the existence of common ground - it more clearly calls out the contrived nature of such thinking.

It might be cynical but I suppose that false dilemma has been popularly adopted simply because dilemma is close enough, and for the most part ordinary people don't care for precision as much as convenience and familiarity.

First, the words "trilemma" and "multilemma" have been used. I know. I did it in a freshman writing class in 1982-3. They were footnoted with explanation as to their meaning relative to "dilemma". Since I was an avid Latin student circa 1970, using "dilemma" when there are multiple unpleasant choices went against the grain. The adjunct, a bitter wannabe, let these variation pass without comment.

As to "dissection", the prefix in this case is not "di-", meaning "two", but "dis-" meaning apart, as in "discombobulated".

Classically, the expression was "on the horns of a dilemma".

When you had to choose between two equally unattractive options, it was described with reference to a mythical two-horned beast.

I'm sure your dictionary is going with the current usage, which allows more than two options.

If we can believe Wikipedia, the story is described here

A dilemma is just an (unpleasant/difficult) choice, and most such choices involve only two options, but that does not mean that they can only have two options.

I suppose it was made worse with the "on the horns of" precursor, because most beasts only have two horns, but the horns don't represent the choices, they represent the unpleasantness. "On the spike of a dilemma" would work just the same.

Fred's dilemma: Should he do A, B, C, or D? No problem.

I've seen similar a similar error with "dissect", where people believed it meant "cut in two".

As an updated dictionary indicated to you, and as other sources demonstrated to me, too, the word dilemma can be used for more than two alternatives.

You can view it as if you're using it in a recurring binary sense, where you have more than two options but you are considering them all in pairs over and over again, until you've covered them all, kind of how some programming languages find the largest number in a set of numbers, if you've ever read about some algorithms for this computational process.

Moreover, another way of referring to the false dilemma fallacy is to call it the fallacy of the excluded middle. And clearly, the "middle" does not necessarily have to be only between two extremes; it can also be between two sets of extreme options.

And by way of this, treating a literal "dilemma" as something that tolerates more than just two options can help us realize a third, previously unknown option. These are not just my own philosophical thoughts about it; I refer you to this phrase from Dictionary.com's web page on the word dilemma, "But even logicians disagree on whether certain situations are dilemmas or mere syllogisms." And the Usage note section of the same source will help you see, without doubt, that this is the correct, modern understanding of the word dilemma.