Интеллектуальная игра начинается сегодня.

Because it is an adjective describing игра, and игра is:

• feminine
• singular
• in the nominative case

Russian adjectives must agree with the noun they describe. So:

• masculine: интеллектуальный
• feminine: интеллектуальная
• neuter: интеллектуальное
• plural: интеллектуальные

Since игра is feminine singular, интеллектуальная is the correct form.

Because игра is the subject of the sentence — it is the thing that is starting.

In Интеллектуальная игра начинается сегодня, the structure is basically:

• Интеллектуальная игра = the intellectual game
• начинается = begins / is starting
• сегодня = today

Subjects are usually in the nominative case, so игра stays in its dictionary form.

Начинается means begins, is beginning, or is starting.

It comes from the verb начинаться, which is the intransitive/reflexive partner of начинать.

A useful comparison:

• начинать что-то = to start something
• начинаться = to begin / to start

So:

• Учитель начинает урок. = The teacher starts the lesson.
• Урок начинается. = The lesson begins.

In your sentence, the game itself is the thing beginning, so Russian uses начинается.

The -ся ending is a reflexive marker, but in many verbs it does not mean literally oneself. Here it is part of the verb начинаться, which means to begin.

This is very common in Russian:

• открывать = to open something
• открываться = to open
• закрывать = to close something
• закрываться = to close
• начинать = to start something
• начинаться = to begin

So in this sentence, -ся helps show that the action is happening to the game itself, not that someone is actively starting another object.

Grammatically, начинается is present tense.

However, in Russian, present tense of an imperfective verb is often used for a scheduled or near-future event, especially when there is a time word like сегодня.

So this sentence can mean:

• The intellectual game begins today
• The intellectual game is starting today

This is similar to English sentences like:

• The movie starts tonight
• School begins tomorrow

So it is present in form, but it can refer to a planned future event.

Yes, absolutely.

Начнётся is the perfective future form of начаться. It also means will begin.

The difference is mainly one of aspect and nuance:

• начинается сегодня = is starting today / begins today
  
  • often sounds like a scheduled event
  • slightly more process-oriented or timetable-like
• начнётся сегодня = will begin today
  
  • more straightforward future result

Both are natural. In many situations, either one could work.

Russian word order is flexible, and the end of the sentence often carries important or new information.

So:

• Интеллектуальная игра начинается сегодня.
  Neutral: the intellectual game begins today.
• Сегодня начинается интеллектуальная игра.
  More emphasis on today.
• Начинается сегодня интеллектуальная игра.
  Possible, but less neutral and more marked.

English relies more on fixed word order. Russian uses word order more for emphasis, focus, and style.

Yes, it is a normal phrase in Russian. Literally it means an intellectual game, but in actual usage it often refers to something like:

• a quiz
• a trivia competition
• a brain game
• a knowledge-based contest

So it does not necessarily mean a philosophical or highly abstract game. It often means a game where people use knowledge, logic, or quick thinking.

A standard stress pattern is:

• интеллектуа́льная
• игра́
• начина́ется
• сего́дня

So the whole sentence is pronounced roughly like:

intellektuAHLnaya igrAH nachinAYet-sa syeVOd-nya

A few things to notice:

• г in игра is a hard g
• -ется in начинается is pronounced something like -yetsa
• unstressed vowels are reduced, especially in normal speech

Russian has no articles like a or the.

So Интеллектуальная игра can mean:

• an intellectual game
• the intellectual game

You understand which one is meant from context.

In this sentence, English will often use the if a specific event is already known, but Russian does not need a separate word for that.

Yes.

Russian present tense often covers both ideas that English separates:

• begins
• is beginning
• is starting
• sometimes even a scheduled future starts

So Интеллектуальная игра начинается сегодня can be translated in several natural ways depending on context.

Russian is not making the same strict distinction here that English sometimes makes between simple present and present continuous.

Possibly, yes — if the context shows that интеллектуальная игра refers to a quiz-like event.

A very literal translation is The intellectual game starts today, but in smoother English, a translator might choose:

• The quiz starts today
• The trivia game starts today
• The competition starts today

So the best translation depends on what kind of event it actually is.