Выбор, будь то блиц-раунд или тай-брейк, важен.

It is a fixed expression meaning something like:

• whether it be ... or ...
• be it ... or ...
• sometimes simply whether it's ... or ...

So in this sentence, будь то блиц-раунд или тай-брейк means that the statement applies in either case.

Yes, historically будь is the imperative singular of быть, meaning be.

But in modern Russian, будь то is mostly felt as an idiomatic set phrase, not as a literal command. So here it does not sound like someone is ordering anything. It functions more like a conjunction-like expression meaning whether it be.

A useful point for learners:
будь то usually stays exactly this way, even if the surrounding noun is plural.

In this sentence, it is best not to translate то separately. It is part of the fixed expression будь то.

So rather than thinking word by word, learn будь то as one unit with the meaning whether it be / be it.

Because Russian normally omits the present-tense form of to be.

So:

• Выбор важен = The choice is important

Russian does not usually say Выбор есть важен in normal modern speech. The idea of is is simply understood.

Because важен is the short form of the adjective важный, and short forms are commonly used when the adjective is the main predicate of the sentence.

Compare:

• важный выбор = an important choice
  
  • full form, used attributively before the noun
• выбор важен = the choice is important
  
  • short form, used predicatively

Here выбор is masculine singular, so the short form is важен.

After будь то, Russian usually names the alternatives in their basic dictionary form, which is normally the nominative.

So:

• блиц-раунд
• тай-брейк

are simply the two named possibilities.

They are not being governed by a preposition here, and they are not taking some case from the main clause. The phrase works more like whether it be X or Y, where X and Y are just being identified.

Because this whole phrase is an inserted parenthetical construction.

The main statement is:

• Выбор важен.

The middle part:

• будь то блиц-раунд или тай-брейк

is extra information specifying the alternatives, so it is set off with commas.

Yes, a little. It is perfectly normal Russian, but it sounds somewhat more literary, formal, or polished than the simplest everyday phrasing.

A learner should recognize it easily in writing, journalism, and formal speech. In very casual speech, people may choose simpler constructions, but будь то is still common and natural.

They are borrowed compound nouns, written with a hyphen, and they are normally treated as masculine inanimate nouns.

Yes, they can decline. For example:

• блиц-раунд → блиц-раунда, блиц-раунду
• тай-брейк → тай-брейка, тай-брейку

In your sentence, they appear in the nominative singular because they are being listed as the alternatives after будь то.