Learn Hardcore Chinese: zhècì bǐsài de chénggōng duì tā láishuō hěn zhòngyào. - The success of this competition is very important to him.

Both are natural; the meaning is the same, with a slight difference in what comes to the listener’s ear first (topic first vs. affected person first).

Why is 的 used between 比赛 and 成功? What does 比赛的成功 mean exactly?

的 is linking 比赛 to 成功 in an attributive (possessive/“of”) way.

比赛 – the competition / match
成功 – success
比赛的成功 – the success of the competition / the competition’s success

Here, 这次比赛的成功 means “the success of this competition (this time)”.

General pattern:
Modifier + 的 + Noun

Examples:

中国的文化 – the culture of China
老师的书 – the teacher’s book
他昨天的表现 – his performance yesterday

So 这次比赛的成功 is a noun phrase: a “thing” (the success) being talked about, not an action.

Could we say 这次比赛成功对他来说很重要 without 的? What would change?

Yes, you can say 这次比赛成功对他来说很重要, but the structure and nuance change:

这次比赛的成功 = “the success of this competition” (noun phrase)
这次比赛成功 = “this time, the competition succeeded / was successful” (verb/adjective phrase: 比赛 is the subject; 成功 is predicate “was successful”)

So:

这次比赛的成功对他来说很重要。
– The success of this competition is very important to him. (emphasis on the “success” as a result, a thing)
这次比赛成功，对他来说很重要。 (usually with a pause or comma)
– That this competition was successful is very important to him.

With 的, you’re clearly talking about the result (success) as a noun.
Without 的, it more naturally sounds like a clause: “the competition was successful.” Both are understandable, but with 的 is more standard and smoother for this sentence.

Why is 很 needed before 重要? Can we just say …对他来说重要?

Grammatically, you can say 对他来说重要, and people will understand you. However, in natural modern Mandarin:

When an adjective is used as the main predicate (like 重要, 高, 静, etc.), speakers almost always put some adverb before it, especially 很.
In many cases, 很 does not strongly mean “very”; it often just smooths the sentence and marks the adjective as a descriptive predicate, almost like a neutral “is”.

So:

对他来说很重要。 – For him, (it) is important. (could be “very important” or just “important” in context; 很 is often light)
对他来说重要。 – Grammatically OK, but can sound a bit abrupt or slightly emphatic/contrastive, as if you’re stressing “(it’s) important (as opposed to not important)”.

Beginner rule of thumb:
When using an adjective as your main verb “to be X”, it is safest/natural to put 很 (or another degree word) before it:

今天很冷。
这个地方很安静。
这次比赛的成功对他来说很重要。

What is the difference between 这次 and 这个, and why is 这次 used here?

这次 = this time / this occasion
这个 = this (one) (general demonstrative for nouns)

Here, 比赛 is an event, something that happens at a time. It’s natural to count it by 次 (times, occurrences):

一次比赛 – one competition (one time a competition happens)
这次比赛 – this (time’s) competition / this competition (this occasion)

If you said 这个比赛, it’s not strictly wrong in casual speech, but it sounds less standard and more influenced by English “this competition”. Native speakers much prefer:

这次比赛
or 这场比赛 (using 场, another common measure word for events like matches, performances, battles)

So 这次比赛 emphasizes “the competition this time / this particular instance of the competition.”

What exactly does 成功 mean here? Is it like “to win”? How is it different from 胜利?

成功 as a noun here means “success”; as a verb/adjective, “to succeed / be successful.”

In 这次比赛的成功, it’s a noun: “the success of this competition”.

Differences:

成功 – success in a broad sense; achieving a goal, things turning out well
- 比赛很成功。 – The competition was very successful. (maybe well-organized, good results, etc.)
胜利 – victory; winning (especially in contests, wars, games)
- 我们取得了胜利。 – We achieved victory / We won.
- 比赛的胜利 – the victory in the match

So:

If you want to stress he/they won the match, 胜利 or 赢 is more direct.
成功 can include winning, but can also mean the event was well-executed, goals were met, etc.

In this sentence, 成功 is more about “the successful outcome” (which may include winning).

What is the basic grammar structure of the whole sentence?

The structure is:

[Topic/Subject] + 对 + [Person] + 来说 + 很 + [Adjective]

Specifically:

这次比赛的成功 – the success of this competition (topic/subject)
对他来说 – for him / as far as he is concerned
很重要 – is very important

So:

这次比赛的成功　对他来说　很重要。
The success of this competition is very important for him.

You can see it as:

X = 这次比赛的成功 (this competition’s success)
Y = 他 (him)
Adj = 重要 (important)

Pattern: X 对 Y 来说很 Adj.
= “As far as Y is concerned, X is very Adj.”

Can I move 对他来说 to the front: 对他来说，这次比赛的成功很重要? Is there any difference?

Yes, that is completely correct and natural:

这次比赛的成功对他来说很重要。
对他来说，这次比赛的成功很重要。

Both are good.

Subtle differences:

Starting with 对他来说 brings the person’s point of view to the foreground:
“For him, the success of this competition is very important.”
Starting with 这次比赛的成功 foregrounds the success itself:
“The success of this competition is very important to him.”

In everyday conversation, they are almost interchangeable; the choice is mostly about what you want to highlight first.

Is 来说 always necessary after 对他? Can I just say 这次比赛的成功对他很重要?

Yes, you can say:

这次比赛的成功对他很重要。

This is also very natural.

Differences:

对他来说 – “for him / from his point of view”; emphasizes the person’s perspective.
对他 – “to him / for him / with regard to him”; slightly more neutral.

Both patterns are common:

对他来说，这件事很难。 – As far as he’s concerned, this matter is difficult.
这件事对他很难。 – This matter is difficult for him.

In your sentence, 对他 and 对他来说 both work, with 对他来说 sounding a bit more explicitly like “from his standpoint.”

How would I say this more colloquially in spoken Chinese? Are there simpler variants?

A few common colloquial equivalents:

这次比赛对他很重要。
– This competition is very important to him.
(Focus on the competition itself, not explicitly on its “success.”)
这次比赛他特别看重。
– He really values this competition.
(More idiomatic; 看重 = “to value, to attach importance to.”)
这次比赛的结果对他来说很重要。
– The result of this competition is very important to him.
(If you want to be explicit about the outcome.)

But your original sentence 这次比赛的成功对他来说很重要。 is already natural, especially in slightly more formal or written contexts.