Kænskan er mikilvæg í samvinnuspilinu.

The base noun is kænska, which means cleverness / shrewdness / cunning.

The ending -n is the Icelandic definite article, which is usually attached to the noun instead of being a separate word like English the. With many feminine nouns ending in -a, the nominative singular definite form looks like -an:

• kænska = cleverness, cunning
• kænskan = the cleverness, the cunning

So Kænskan er mikilvæg... is literally something like The cleverness is important...

It can be either, depending on context.

Kænska often suggests shrewdness, craftiness, tactical cleverness, resourcefulness. In some contexts it can sound slightly sly, like cunning in English. But in a sentence about a game, it is usually understood more positively or neutrally: smart thinking or strategic cleverness.

So in this sentence, it most likely means something like cleverness / tactical skill rather than anything morally bad.

Because Icelandic adjectives agree with the noun they describe in gender, number, and case.

Here, kænskan is:

• feminine
• singular
• nominative

So the adjective also appears in the feminine singular nominative form:

• masculine: mikilvægur
• feminine: mikilvæg
• neuter: mikilvægt

That is why the sentence has Kænskan er mikilvæg.

Even though the adjective comes after er, it still agrees with the subject.

This is about two things at once:

1. í can take different cases
2. samvinnuspilinu is a declined definite noun

With í:

• í + dative = in a place/state/location
• í + accusative = into something, movement toward/into

Here the meaning is in the cooperative game, not into the cooperative game, so Icelandic uses the dative.

The noun is samvinnuspil:

• nominative singular: samvinnuspil
• dative singular: samvinnuspili
• dative singular definite: samvinnuspilinu

So í samvinnuspilinu means in the cooperative game.

It is a compound word, which is very common in Icelandic.

It is built from:

• samvinna = cooperation
• spil = game

Together they form samvinnuspil = cooperative game

Then Icelandic adds the case ending and the definite article:

• samvinnuspil = cooperative game
• samvinnuspili = in a cooperative game / to a cooperative game, depending on context
• samvinnuspilinu = in the cooperative game

So the whole word packs in a lot of information that English would usually spread across several words.

Yes, and it would change the nuance a bit.

• Kænska er mikilvæg í samvinnuspili = Cleverness is important in a cooperative game or in cooperative games
• Kænskan er mikilvæg í samvinnuspilinu = The cleverness is important in the cooperative game

The version without the definite article sounds more general.
The version in your sentence sounds more specific or connected to a particular game or a particular kind of cleverness already being discussed.

So both can be possible, depending on context.

Because this is a simple main clause, and in this kind of sentence Icelandic can look very English-like.

The structure is:

• Kænskan = subject
• er = verb
• mikilvæg = predicate adjective
• í samvinnuspilinu = prepositional phrase

So it is basically:

Subject + is + adjective + prepositional phrase

Icelandic does have its own word-order rules, especially the verb-second pattern in main clauses, but in a straightforward sentence like this, the order looks very familiar to an English speaker.

A rough learner-friendly pronunciation guide would be:

KINE-skan er MIH-kil-vigh i SAM-vin-nu-spi-li-nu

A few helpful notes:

• æ in kænskan is roughly like eye
• á/í/ú-style long vowels are important in Icelandic, but here the main thing is just getting the general shape right
• samvinnuspilinu has clear parts: sam-vinnu-spili-nu
• the g in mikilvæg is not a hard English g like in go

A more natural Icelandic pronunciation will take practice, but if you can clearly separate the parts of the compound and remember that æ sounds roughly like eye, you will already be much closer.