قواعد اللعبة وترتيب اللعب مهمان.

Because Arabic usually leaves out the present-tense verb to be in sentences like this.

So:

قواعد اللعبة وترتيب اللعب مهمان

literally looks like:

the rules of the game and the order of play important

but it naturally means:

The rules of the game and the order of play are important.

If you wanted were or will be, Arabic would normally use an actual verb.

Because both are the first noun in an idafa construction, which is the Arabic possessive/genitive construction.

• قواعد اللعبة = the rules of the game
• ترتيب اللعب = the order of play

In an idafa, the first noun usually does not take الـ. The whole phrase becomes definite because the second noun is definite.

So قواعد اللعبة is definite even though قواعد itself has no الـ.

Both are idafa phrases:

• قواعدُ اللعبةِ
• ترتيبُ اللعبِ

In this structure:

• the first noun is the main thing being talked about
• the second noun specifies it
• the second noun is in the genitive case

So:

• قواعد اللعبة = rules of the game
• ترتيب اللعب = order of play

This is one of the most common noun patterns in Arabic.

They are related, but they are not the same word.

• اللعبة means the game
• اللعب means play / playing

So the sentence combines two different ideas:

• قواعد اللعبة = the rules of the game
• ترتيب اللعب = the order of play

Even though both come from the same root, they function differently here.

قواعد is the plural of قاعدة, meaning rule or base/foundation, depending on context.

Here it means rules.

This is a broken plural, which means the plural is formed by changing the internal pattern of the word, not just by adding a regular ending.

• singular: قاعدة
• plural: قواعد

Because the sentence is treating the subject as two coordinated things:

1. قواعد اللعبة
2. ترتيب اللعب

Since there are two items joined by و (and), Arabic can use the dual in the predicate:

• مهمان = important for two things

So the meaning is roughly:

The rules of the game and the order of play are both important.

That is a very good question.

If you had only:

قواعد اللعبة

then it would be very normal to say:

قواعد اللعبة مهمة = The rules of the game are important

That is because non-human plurals often take feminine singular agreement in Arabic.

But in your sentence, قواعد اللعبة is joined with ترتيب اللعب. Now the speaker is talking about two units together, so the predicate agrees with the pair as dual:

قواعد اللعبة وترتيب اللعب مهمان

Also, because one of those two units is masculine (ترتيب), the dual agreement appears in the masculine dual form.

Because it is the predicate of the sentence, not an adjective directly attached to a noun.

Arabic often uses an indefinite predicate after a definite subject:

• البيت كبير = The house is big
• الولد ذكي = The boy is smart
• قواعد اللعبة وترتيب اللعب مهمان = The rules of the game and the order of play are important

If you made it definite with الـ, it would no longer sound like the normal predicate pattern here.

Because it is dual nominative.

In this sentence, مهمان is the predicate of a nominal sentence, so it is in the nominative case. The dual nominative ending is:

• ـان

The dual accusative/genitive ending is:

• ـين

So here:

• مهمان = correct for nominative

If the grammar of the sentence required accusative or genitive, you would expect ـين instead.