Someone please explain to me why the above question is correct as written... instead of 'How do you dare?'.

It's a remnant of an old grammatical construct. It's (in that usage) called a "modal verb". Formally it modifies a phrase that includes another verb, however sometimes the entire phrase is sometimes implied: How dare you!

We get the same syntax in a lot of other somewhat-canned phrases with modal verbs:

Must you?
Need I continue?
Wilt thou take this woman... (a really long sentence followed by a short sentence, a long sentence, and a life sentence)

If Wikipedia is to be believed (http://en.wikipedia.org/wiki/Modal_verb#English), a modal verb implies probability - such as must, can, should. I don't know if it includes "how dare you" or "need I continue"? Though the latter is pretty close to "must I continue" / "should I continue".

I wonder if "how dare you" is similar to "I have not" in slightly archaic English. As in "I have not the ring that you seek" instead of "I do not have ..." and "how dare you imply that I swallow pretzels" instead of "how do you dare to imply..." In both case, the auxiliary verb "do" is skipped.

As in "I have not the ring that you seek" instead of "I do not have ..." and "how dare you imply that I swallow pretzels" instead of "how do you dare to imply..." In both case, the auxiliary verb "do" is skipped.

As well sa the word "to"

I agree it's probably related to older, more formal English.

LWW