Learn English – the dinner vs. dinner (grammar question)

The definite article is definitely NOT required, as stated by the previous commenter, and is actually more common and natural without it, i.e. Let's discuss Russian grammar. The use of the definite article here is not incorrect, however it is superfluous and awkward, at least to my ear.

In another context, one would say: I'm having trouble with Russian grammar. If one said the Russian grammar here, it would call to mind the grammar textbook, since this is also called a grammar.

Also note the following: Let's discuss...

• Russian pronunciation, BUT the Russian sound system (or phonology)
• Russian syntax OR Russian word order [no article]
• Russian semantics BUT the Russian mentality
• Russian vocabulary BUT the Russian lexicon

I personally would not use "the" in the sentence, since the narration refers to the usual cycle/habitual action during Elsie's early years (when she's nine years old).

BUT

Because the narration also gives specific actions, I take it that the author wants to point out that Elsie is specifically cooking dinner, and that she's not cooking eggs, nor "midnight" meal, nor any other meal/cuisine or equivalent. Nothing (else) but dinner.

Note:

I think it's best to add @user3169's comment here.

"Dinner could be countable or uncountable. That specific dinner, or the meal you eat in the evening in general. In your example, it is talking about general activities, so I would expect no article (other than for emphasis perhaps)."