Ведущий игры уточнил формулировку вопроса.

Because ведущий can function as a noun in Russian, not just as an adjective or participle.

Here it means the host / presenter / moderator of the game.

Grammatically, it looks like an adjective, but in this sentence it is being used substantively:

• ведущий = host, presenter
• игры = of the game

So ведущий игры means the game host.

This is very common in Russian:

• ведущий программы = the host of a program
• ведущая шоу = the female host of a show

Игры is genitive singular of игра.

It is in the genitive because it depends on ведущий and shows what kind of host this is:

• ведущий игры = host of the game

This is similar to English of:

• директор школы = director of the school
• начало фильма = beginning of the film
• ведущий игры = host of the game

So the genitive here answers the question ведущий чего? — host of what?

Because it is the direct object of the verb уточнил.

The verb уточнить means to clarify / to specify / to refine, so it takes something that is being clarified:

• уточнил что? = clarified what?
• формулировку = the wording

The dictionary form is формулировка, but in the accusative singular it becomes формулировку.

So:

• формулировка = wording, phrasing
• уточнил формулировку = clarified the wording

Because вопроса depends on формулировку.

The phrase формулировка вопроса means:

• the wording of the question
• literally: wording of a question/the question

So this is another genitive relationship:

• формулировка чего? = wording of what?
• вопроса = of the question

This gives us a noun phrase inside a noun phrase:

• ведущий игры = host of the game
• формулировку вопроса = wording of the question

Because уточнил is perfective, while уточнял is imperfective.

• уточнил = clarified, specified, made more precise
  → one completed action
• уточнял = was clarifying, used to clarify, clarified (process/repetition)

In this sentence, the idea is that the host performed a completed action: he clarified the wording.

So уточнил is the natural choice.

Compare:

• Ведущий уточнил формулировку вопроса.
  = The host clarified the wording of the question.
• Ведущий уточнял формулировку вопроса.
  = The host was clarifying the wording of the question / spent time clarifying it.

Russian uses case endings, not just word order.

Here:

• ведущий is nominative singular → the subject
• формулировку is accusative singular → the direct object
• игры and вопроса are genitive singular → dependent nouns

So even if the word order changed, the grammar would still show the roles.

For example:

• Ведущий игры уточнил формулировку вопроса.
• Формулировку вопроса уточнил ведущий игры.

Both still mean essentially the same thing, though the emphasis changes.

That is the normal past tense marker in Russian.

Russian past tense is usually formed from the infinitive stem plus -л, and then it agrees in gender and number:

• masculine: уточнил
• feminine: уточнила
• neuter: уточнило
• plural: уточнили

Since ведущий is masculine singular, the verb is:

• ведущий уточнил

If the subject were feminine:

• ведущая игры уточнила формулировку вопроса

Yes, it is a common word in formal, academic, journalistic, and quiz/test contexts.

Формулировка means:

• wording
• phrasing
• sometimes formulation

In this sentence, wording or phrasing is usually the most natural English equivalent.

Examples:

• неудачная формулировка = poor wording
• точная формулировка = precise wording
• изменить формулировку = change the wording

So формулировку вопроса is very naturally the wording of the question.

Yes, depending on context.

The Russian phrase itself is fairly neutral:

• ведущий = host / presenter / moderator

Possible English translations depend on the situation:

• host if it is a TV/game show context
• quizmaster if it is a quiz or trivia setting
• game master in some gaming contexts
• presenter in a broadcast context

So the exact English word depends on what kind of игра this is.

Yes. Russian word order is flexible because the cases show the grammatical roles.

Possible variants:

• Ведущий игры уточнил формулировку вопроса.
• Формулировку вопроса уточнил ведущий игры.
• Уточнил формулировку вопроса ведущий игры.

These all mean roughly the same thing, but the emphasis changes:

• sentence-initial ведущий игры focuses more on the subject
• sentence-initial формулировку вопроса focuses more on what was clarified
• sentence-initial уточнил can sound more narrative or stylistically marked

The version you were given is the most neutral.

The standard stresses are:

• веду́щий
• игры́
• уточни́л
• формулиро́вку
• вопро́са

So the whole sentence is:

Веду́щий игры́ уточни́л формулиро́вку вопро́са.

Stress matters in Russian, so it is worth learning these with the words.

Yes, it is completely natural.

It sounds slightly formal or neutral because of words like уточнил and формулировка, but that is exactly what you would expect in contexts like:

• quizzes
• competitions
• classroom tasks
• interviews
• TV shows
• official speech

A more casual version might use simpler wording, but this sentence is perfectly normal and idiomatic.