Is “curate the market” common usage of “curate”?

That is a rather odd use of the word "curate" in the verb form, as their particular usage may change what they intended the sentence to mean. I doubt that they meant to imply that the publisher has great power over the market and actively controls it, rather than merely participates and contributes to it.

Also, the definitions that you found for "curate" are probably a result of poor website design on behalf of those dictionary makers. The first definition should be for the verb form rather than for the noun; and in fact Oxford Languages says that the noun version of "curate" is archaic, but they still list it first. The better definition is for the verb form: "select, organize, and look after the items in (a collection or exhibition)." Those dictionary webpages now do list that additional form of the word and the definitions on the entry for the word, though it is lower down.

Regarding if you should use "curate" in the way they did, I would suggest against it. Curate is most commonly used when talking about a manager, supervisor, overseer or maintainer of a collection or some form of historic or artistic entity - often a museum. Though you could say "you must curate the offer letter that we will send to the applicant we selected" - to imply that they should take great care when writing the letter. A poet is the curator of the words they put in their poem. This stretches the definition, but it is respectful to the formal definition, and is used to emphasize the care that the person puts into the work.

I see this question was asked in 2013. It looks like the NY Times author may have absorbed a contemporary jargon-y use of "curate" from prevailing trends in retail. This page includes the comment:

Curated shopping means that you are creating unique selections of products for your customers based on their interests and their previous behavior as shoppers. This is a trend that has become highly popular starting around 2013 and which is more important than ever due to the current nature of retail. While the term is very often applied to ecommerce, it can in fact apply to any kind of commerce.

There are other examples of "curated" meaning designing the product mix presented to consumers.

When I read the phrase "Your Publisher creates book’s mold ahead of time, in so far as it curates the existing market into which book must fit. " I understood this to reflect specific decisions of the publisher. They choose which imprint in their stable will appear on the book's spine. Within that imprint, they choose a genre. Is the book general literature or fantasy? General literature or young adult? These decisions determine if the book will appear in airport newsstands; or in a specific section of a brick-and-mortar store, and the kind of casual reader who might buy it on speculation.