Drengen spiller brætspillet.

Because Danish usually marks the by adding it to the end of the noun.

• dreng = boy
• drengen = the boy

This is called the postposed definite article.
For many common-gender nouns, the definite ending is -en.

So instead of a separate word like English the boy, Danish often says drengen.

For the same reason: the noun is in the definite form.

• brætspil = board game
• brætspillet = the board game

Here the ending is -et, not -en, because spil is a neuter noun.

A useful pattern is:

• common gender: often -en in the definite singular
• neuter gender: often -et in the definite singular

So drengen and brætspillet both mean the ..., but they take different endings because the nouns belong to different genders.

Because in Danish, when a noun stands alone in the definite form, the is usually attached as an ending.

So:

• drengen already means the boy
• brætspillet already means the board game

You do not normally say a separate the before these nouns in this kind of sentence.

Spiller is the present tense of spille = to play.

Danish verbs are much simpler than English verbs in this way: the verb usually has the same form for all persons in the present tense.

So you get:

• jeg spiller = I play / I am playing
• du spiller = you play / you are playing
• han spiller = he plays / he is playing
• drengen spiller = the boy plays / is playing

Unlike English, Danish does not add a special -s for he/she/it.

It can mean either, depending on context.

Danish present tense often covers both:

• he plays
• he is playing

So Drengen spiller brætspillet could mean:

• The boy plays the board game
• The boy is playing the board game

Usually the surrounding context tells you which is intended.

Because this is a normal Danish main clause with the usual subject–verb–object order:

• Drengen = subject
• spiller = verb
• brætspillet = object

So the pattern is:

The boy + plays/is playing + the board game

That is very similar to English in a basic statement.

It is one word, and it is a compound noun.

• bræt = board
• spil = game
• brætspil = board game
• brætspillet = the board game

Danish, like German, very often joins nouns together into one compound word. English sometimes writes similar expressions as two words, but Danish commonly prefers one.

A rough guide is:

• bræt sounds somewhat like bret, but with the Danish vowel æ
• spillet sounds roughly like spill-ed, though the final -et is weaker than English would suggest

Very roughly: BRET-spil-et

A few pronunciation notes:

• æ is a front vowel, a bit like the vowel in British trap for some speakers, but not exactly the same
• Danish r can affect nearby vowels
• the t in bræt may be softer than an English learner expects, depending on speaker and style

The safest strategy is to listen to native audio and copy the rhythm as a whole.

A rough approximation is DREN-yen or DREN-gen, depending on how carefully it is spoken.

Important things for learners:

• the first part dreng is not pronounced exactly like it looks to an English speaker
• ng represents the ng sound as in sing
• the definite ending -en is often pronounced lightly

So although it is spelled drengen, the spoken form may sound smoother and more reduced than an English learner expects.

You need to know the noun’s gender.

Danish has two grammatical genders:

• common gender
• neuter

Examples here:

• en dreng = a boy → drengen = the boy
• et brætspil = a board game → brætspillet = the board game

So the indefinite article helps you learn the gender:

• if a noun is learned with en, its definite singular is often -en
• if a noun is learned with et, its definite singular is often -et

That is why it is very helpful to memorize nouns with their article:

• en dreng
• et brætspil

Yes. That would mean The boy is playing a board game.

Compare:

• Drengen spiller brætspillet = The boy is playing the board game
• Drengen spiller et brætspil = The boy is playing a board game

So the difference is the same as in English:

• the = a specific one
• a/an = one, not specified

Because the definite ending already does the job.

In simple cases, Danish normally says just:

• brætspillet = the board game

Using det directly before it would not be correct here.

However, if there is an adjective, Danish often uses both a separate determiner and the definite ending:

• det store brætspil = the big board game

So:

• no adjective: brætspillet
• with adjective: det store brætspil

No. Spille is used for several kinds of play in Danish, including:

• playing a game
• playing music or an instrument
• acting/performing in some contexts

In this sentence, because the object is brætspillet, it clearly means play a board game.

So spiller is a very common and flexible verb, much like English play, but you still have to learn its common patterns from usage.