In addition to its role signifying an upper limit as a superlative or indicating a majority, the word “most” also enjoys a more relaxed usage as an intensifier. This is the meaning intended in your example:

most

ADVERB

3. Extremely; very:

• it was most kind of you
  

• that is most probably correct
  

• That is now no longer a fair representation of their view, and it most certainly is not of mine.
  

• It most certainly was not a life-changing experience, but it did provide amusements.
  

• History will most certainly exact a heavy price from them for being such imbeciles.

_{Source: Oxford Dictionaries definition of “most”}

This equivalence with “very” makes it possible to employ an indefinite article or no article at all, depending on what you are describing. The ODO examples above give a good sense of when you would not use an article, but in your example the author uses an indefinite article.

• It attempts to explain the origin of Captain Hook, Peter, the Lost Boys and the rest of what we know from the famous story. It is done in a most entertaining way with a very talented cast. During its New York run, the New York Times wrote that it is “the most exhilarating storytelling on Broadway in decades.” Praise like that has to be earned from that publication.
  _{Source: Applefeld, Eddie. "Peter Pan’s Prequel Opens in Baltimore." Baltimore Post-Examiner, 19 May 2014.}

This example is a good comparison of an indefinite article and a definite article usage.

The first “most” in the quotation is equivalent with “very”, so you treat it the same way as you would any description of a generic thing. The subject is “way”, and this very entertaining way is just one of many very entertaining ways in which these origins might be explained.

The second “most” is used in the usual superlative way that you were expecting when you read the passage you cited. The author of the NYT review is making the claim that this musical is the most exhilarating storytelling in decades, so the definite article must be used to single out the storytelling in this musical as being the single best storytelling in at least 20 years.