The answer to the question “Why is dark an adverb in this sentence?” is that it is not one; that source is wrong. That’s because dark cannot ever be an adverb, let alone here. It’s just that color-words can behave somewhat curiously.

We have various related questions about this curiosity, including this one. John Lawler’s suspicion about color words having a special dispensation seems instructive:

John Lawler: Blue is the name of a color; names are usually nouns. I suspect we have a special dispensation for color words, like we do for many other semantically-crucial word sets.

Greg Lee: @JohnLawler, of course "blue" is a noun. I would never deny that, nor does McCawley. That's why, he reasons, it can be modified by the adjective "dark".

So it seems colors can be nouns for modification purposes in that they take adjectives to qualify them. The resulting multiword compound, the adjectivally qualified color like dark red or robin’s egg blue, is used to further describe another noun. The whole compound can then be qualified by intensifiers like very.

_{I'm guessing that we can use adjective ordering rules and perhaps constituency tests to show that the whole multiword part about the color counts as one single syntactic constituent. Therefore you must look at grammatical roles these phrases play in the grammar, not at the internal parts of speech of individual words within that phrase. Otherwise you get nonsense results the way you get when a gerund clause’s head VERB-ing word gets mistakenly called a noun when it’s really a verb. Calling it a noun is a common error — but calling is only a verb there at the start of this sentence, not a noun. I suspect this is the same class of error in calling dark an adverb when it’s actually an adjective.}

What the Dictionary says...

Regarding blue, the OED says:

Often with modifying word indicating intensity (as bright blue, dark blue, light blue, etc.), drawing a comparison with an object or another colour (as indigo blue, lavender blue, powder blue, etc.), or making a (sometimes arbitrary) association with a person or thing (as French blue, royal blue, navy blue), etc.

But those “qualifying words” certainly are not adverbs. Indeed, the OED says that dark is an adjective when it has this color-related sense:

3c. Prefixed, as a qualification, to adjectives of colour: Deep in shade, absorbing more light than it reflects; the opposite of light. (Usually hyphened with the adj. when the latter is used attributively.)

And here are two citations provided of this:

• 1859 J. Ruskin Two Paths v. 202
  That lovely dark purple colour of our Welsh and Highland hills is owing, not to their distance merely, but to their rocks.
• 1863 M. L. Whately Ragged Life Egypt xvii. 163
  Clad in the ordinary dark-blue drapery.

Rubber Baby Buggy Bumpers

Why do they say this is an adjective? If you think it through, you’ll see why dark cannot be an adverb here, only an adjective.

What’s your favorite color?
Hot pink.
You mean like your hot pink sunglasses?
Exactly! All my sunglasses are hot pink!

If someone tells you their favorite color is hot pink, it seems reasonable to call pink a noun and hot an adjective. But now applying that to sunglasses doesn't swap around all the parts of speech into something new.

This happens with colors all the time:

• cerulean blue skies
• cherry red sunsets
• cobalt blue skies
• safety green vests
• royal purple stoles
• saffron yellow robes
• robin's egg blue eyes
• electric pink sunglasses

The last word in each of those noun phrases is a noun, but the first word of each is not an adverb. It is either a noun or an adjective in each case. Cobalt is a noun; it does not suddenly become an adjective when talking about a cobalt blue nor does it become an adverb when it is used in our cobalt blue skies

This is just like how tinted is not an adverb in tinted glass windows, or like how in the whole tongue-teaser rubber baby buggy bumpers, there are no adverbs nor even any adjectives.