In the year 2014, Uzbekistan's chemical production grew by 9% relative to 2013. In the period under report, the companies engaged in the field increased their outputs of the following products: potassium chloride (+14%), sodium nitrate (+18%) ...
1 Is the definite article necessary?
By including it, you are making a definite reference to companies engaged in the field. By making a definite reference you are referring to all the companies unless you otherwise state that you are not.
Not including Company Firth, the companies engaged in the field...
2 Would [leaving no article] make it seem as if some companies' outputs are not included in the aggregate figures?
First, technically speaking you are not "leaving no article" or even "using no article." You are using the zero-article rather than the definite article. The zero-article before a plural count noun is an indefinite reference.
An indefinite reference to a plural count noun with the zero-article is indefinite as to the number of companies. However, this indefinite number can include all the companies.
Whereas, using some companies is also an indefinite reference to companies engaged in the field, and this also means an indefinite number (greater than 1) of companies, some cannot mean all the companies.
Some of his friends in Vladivostok are going to visit him at his home in Petersburg.
The use of some precludes or rules out the possibility, at least grammatically at the time of utterance, that all his friends in Vladivostok are traveling to Petersburg.
Friends of his in Vladivostok are going to visit him...
leaves open the possibility that this indefinite reference includes all his friends.
As far as
On the other hand, it reads a bit like "the companies that we've mentioned previously" due to the use of the.. or maybe I'm wrong.
I wish teachers had never ever come up with this dual notion of (1) a thing previously mentioned takes the and (2) a thing mentioned for the first time takes a/an. Neither statement is true.
I can surmize that the reason it reads a bit like companies we've mentioned previously is because that is one context in which a writer can make a definite reference. But there are plenty of other such contexts, such as yours.
In your discourse, you have used the to make a definite reference because you assume that your readers can uniquely identify which companies you are referring to. Readers can so do from these sources: the complete noun phrase (companies engaged in the field), the context (talking about chemical production in Uzbekistan's chemical production), and general knowledge about the world (chemical production involves companies).
I have read that 75% of uses of the definite article are first mentions. This is because the overwhelming number of first mentions are identifiable from context, shared knowledge, general knowledge, and/or common sense. Just read any magazine or news article in English.
In both fiction, and non-fiction, there is another use of the in first mention, which is to indicate a topic.
I was walking home when I heard the bad news.
What do you think the topic will be in subsequent sentences? :)
On the other hand, one can consider that this use of the is simply a cataphoric definite reference to a referent whose unique identity will be made at a later time in the discourse (in other words, from context).