Hazardo gravas en ĉi tiu tabulludo.

Because it is the subject, and Esperanto often uses subject–verb order, just like English: Hazardo gravas = Chance matters.

Putting hazardo first is also natural because it introduces the main topic. Esperanto word order is fairly flexible, though, so you could also say:

En ĉi tiu tabulludo hazardo gravas.

That would sound more like In this board game, chance matters.

Gravas is the present-tense form of the verb gravi.

• gravi = to matter, to be important
• -as = present tense

So gravas means matters or is important.

This is a normal Esperanto verb, not an adjective.

Because gravi already means to matter / to be important as a full verb.

So Esperanto does not need something like estas grava here, although that would mean something slightly different:

• Hazardo gravas = Chance matters
• Hazardo estas grava = Chance is important

These are close in meaning, but gravas is the more direct way to say matters.

In Esperanto, tiu means that one / that, and ĉi adds the idea of nearness. So:

• tiu = that
• ĉi tiu or tiu ĉi = this

Both word orders are correct:

• ĉi tiu tabulludo
• tiu ĉi tabulludo

Both mean this board game.

Because demonstratives like ĉi tiu already make the noun definite.

In English, you say this board game, not the this board game. Esperanto works the same way:

• la tabulludo = the board game
• ĉi tiu tabulludo = this board game

You do not use la together with ĉi tiu.

Yes, it is one compound word.

It is made from:

• tabulo = board
• ludo = game

Together: tabulludo = board game

Esperanto often builds new words this way. The main idea usually comes at the end, so tabulludo is a kind of ludo.

En usually means in or inside, and here it means in the context of this board game.

So:

• en ĉi tiu tabulludo = in this board game

This is a very natural way to talk about what is important within a game, story, system, situation, and so on.

Because there is no direct object in this sentence.

• Hazardo is the subject.
• gravas is the verb.
• en ĉi tiu tabulludo is a prepositional phrase.

The accusative -n is usually used for a direct object, but gravi does not take one here.

Also, after en, you normally do not use -n unless there is motion toward a place. Here there is no motion, just location/context.

It most often refers to chance, randomness, or luck depending on context.

In this sentence, chance or randomness is probably the best translation, because the sentence is about a board game and how much random factors affect it.

So the idea is something like:

• chance matters
• randomness matters
• luck plays an important role

The exact best English word depends on the situation.

A few useful points:

• ĉ sounds like ch in church
• ĉi is pronounced roughly like chee
• tiu is two syllables: TI-u
• stress in Esperanto goes on the second-to-last syllable

So the sentence is pronounced approximately like:

ha-ZAR-do GRA-vas en chi TI-u ta-bul-LU-do

More exactly by stress:

• hazardo → ha-ZAR-do
• gravas → GRA-vas
• ĉi tiu → ĈI TI-u
• tabulludo → ta-bul-LU-do

Yes, that is grammatical.

It means Chance is important in this board game.

Compared with Hazardo gravas en ĉi tiu tabulludo, it feels a little less direct. The original sentence is the more natural way to say Chance matters in this board game.

So both are possible, but they are not exactly the same in style:

• Hazardo gravas = chance matters
• Hazardo estas grava = chance is important