Learn Russian: Мы не начисляем очков за такие ошибки. - We do not award points for such mistakes.

This is the Genitive of negation. When a transitive verb is negated by не, its direct object often takes the Genitive case instead of the Accusative. This is especially common when emphasizing the complete absence of something (not awarding any points at all) or with abstract nouns.

Where does the verb начисляем come from, and how does it mean 'award'?

The verb начислять is built from the root of число (number) and the prefix на- (onto). It literally means to count onto a balance or tally. It is the standard verb for awarding points in a game, accruing interest, or adding bonuses to an account.

Why use за + Accusative (за такие ошибки) to mean 'for' in this context?

In Russian, за followed by the Accusative case is used for transactions, exchanges, rewards, and penalties. Because the points are being withheld as a penalty 'in exchange' for the mistakes, за is the correct preposition.

Why is the imperfective verb начисляем used here rather than a perfective form?

The imperfective aspect is used because the sentence describes a general, recurring policy (we never award points for these types of mistakes). A perfective verb would imply a single, specific instance of not awarding points.