Learn English – is/has/have + verb-ed

We use "do support" to form questions and negatives only when there isn't already an auxiliary, such as be, have, or a modal.

When have is acting as a lexical verb it may take "do support":

Do you have any milk?

but it doesn't have to, particularly in British English:

Have you [got] any milk?

But when have is an auxiliary, forming a perfect tense, it cannot take "do support":

Has anyone used this before?

not

*Does anyone have used this before?

(You didn't ask about this, but it's worth specifying:) in the phrasal verb have to, meaning be obliged to", have is not an auxiliary, and may take "do support" in questions and negatives:

I don't have to go.

or

I haven't got to go.

You might even find I haven't to go in old books, but I doubt if there's anybody that says it now.

Option B is the correct answer, as your answer key says. The error is in the use of the singular form of the copula "is" with a plural subject.

The correct form of the copula is "are" because the sentence in the non-inverted form is:

Developing the ability to work with others and developing leadership skills are more important than winning.

This is a sentence with a compound subject. That means two subjects, so the plural is used.

Same pattern as:

Trees and bushes are important in gardens.

For clarification, here is the same sentence with the corrected word and with brackets added to contain each subject:

[I returned here to edit brace to brackets and cartouche to contain. I cannot believe I would have used the terms braces and cartouche here.

More important than winning are { developing the ability to work with others } and { developing leadership skills }