Learn Hardcore Greek: Αυτό το παιχνίδι παίζεται εύκολα με δύο ανθρώπους. - This game is played easily with two people.

παιχνίδι is a neuter noun.
The demonstrative αυτός / αυτή / αυτό has three genders:
- masculine: αυτός
- feminine: αυτή
- neuter: αυτό

So we need the neuter form αυτό to match the neuter noun παιχνίδι:
Αυτό το παιχνίδι = This game.
Αυτός would be used with a masculine noun, e.g. Αυτός ο άνθρωπος (this man/person).

Why do we need both αυτό and the article το? Could we just say Αυτό παιχνίδι?

In standard modern Greek, you normally keep the article after a demonstrative:

αυτό το παιχνίδι = this game
εκείνο το παιχνίδι = that game

Leaving out the article (αυτό παιχνίδι) sounds unnatural or stylistically marked, especially in everyday speech. Greek uses the article much more than English, even with demonstratives.

What gender, number, and case is παιχνίδι here, and how does it change?

In Αυτό το παιχνίδι παίζεται εύκολα με δύο ανθρώπους:

παιχνίδι is neuter, singular, accusative (because it is the direct object of the demonstrative αυτό / article το in this structure).
Its basic forms are:
- singular:
  - nominative: το παιχνίδι
  - genitive: του παιχνιδιού
  - accusative: το παιχνίδι
- plural:
  - nominative: τα παιχνίδια
  - genitive: των παιχνιδιών
  - accusative: τα παιχνίδια

Meaning: game, toy (context decides).

What exactly is παίζεται? How is it different from παίζει?

Both come from the verb παίζω (to play).

παίζει = present, active, 3rd person singular
- Το παιδί παίζει. = The child plays / is playing.
παίζεται = present, mediopassive (often called passive), 3rd person singular
- Το παιχνίδι παίζεται. = The game is played / is being played.

So παίζεται corresponds to English is played / is being played. It focuses on the game, not on who is playing it.

Why is the passive voice used here instead of an active sentence?

The passive structure Το παιχνίδι παίζεται… is natural in Greek when:

You want to talk about how a game is generally played,
You don’t care who the players are, only how the game works.

You could also say:

Δύο άνθρωποι παίζουν αυτό το παιχνίδι εύκολα.
= Two people play this game easily.

But that sounds more like a specific situation. The original sentence sounds more like a description in rules or instructions: how the game is normally played.

Could παίζεται mean both is played and is being played right now?

Yes. Modern Greek doesn’t distinguish between simple present and present continuous as clearly as English.

Το παιχνίδι παίζεται εύκολα με δύο ανθρώπους.
- can mean: This game is (generally) easily played with two people.
- in another context, it could also describe what is happening now:
  Το παιχνίδι παίζεται τώρα. = The game is being played now.

Context tells you if it is general or happening at the moment.

Why is it εύκολα and not εύκολο?

Εύκολα is an adverb, derived from the adjective εύκολος.

εύκολος (adj.) = easy
εύκολα (adv.) = easily

In the sentence, εύκολα describes how the game is played:

Το παιχνίδι παίζεται εύκολα.
= The game is played easily.

If you used εύκολο, you would need a different structure:

Αυτό το παιχνίδι είναι εύκολο να παιχτεί με δύο ανθρώπους.
= This game is easy to be played with two people.

So εύκολα fits because it modifies the verb παίζεται.

Can the word order change? For example, can I say Αυτό το παιχνίδι εύκολα παίζεται με δύο ανθρώπους?

Greek word order is flexible, but some orders sound more natural.

Most neutral and common:
Αυτό το παιχνίδι παίζεται εύκολα με δύο ανθρώπους.

You can move εύκολα for emphasis:

Αυτό το παιχνίδι εύκολα παίζεται με δύο ανθρώπους. – possible, but sounds a bit more marked / poetic.
Εύκολα παίζεται αυτό το παιχνίδι με δύο ανθρώπους. – also possible; it emphasizes εύκολα.

For everyday use, stick to the original order; it’s the most typical and clear.

Why do we use με δύο ανθρώπους and not από δύο ανθρώπους?

In Greek:

με = with
από = by / from

Here, με δύο ανθρώπους means the game is played with two people, i.e. it is a game for two players.

Από δύο ανθρώπους would emphasize the agent (who performs the action), like English by two people, and in this context it sounds less natural. The idea of a two-player game is normally expressed with με:

Το παιχνίδι παίζεται με δύο παίκτες.
= The game is played with two players.

Why is it δύο ανθρώπους and not δύο άνθρωποι?

Because με takes the accusative case, and ανθρώπους is the accusative plural of άνθρωπος.

Forms of άνθρωπος (person, human):

singular:
- nominative: ο άνθρωπος
- accusative: τον άνθρωπο
plural:
- nominative: οι άνθρωποι
- accusative: τους ανθρώπους

After με, you must use the accusative: με δύο ανθρώπους (with two people), not με δύο άνθρωποι.

Could we say με δύο άτομα instead of με δύο ανθρώπους? Is there a difference?

Yes, you can say:

με δύο άτομα = with two people / with two persons

Άτομο literally means individual, person and is a bit more neutral/impersonal.
Άνθρωπος literally means human being, person and feels a bit more personal/natural in many contexts.

For a game description, both δύο άτομα and δύο ανθρώπους are acceptable. Depending on context, άτομα can sound a touch more formal or technical.

Why is there no article before δύο ανθρώπους (why not με τους δύο ανθρώπους)?

We leave out the article here because we are talking in general about any two people, not some specific two people already known from the context.

με δύο ανθρώπους = with two people (any two)
με τους δύο ανθρώπους = with the two people (specific ones that we both know who they are)

Game instructions and general descriptions usually use the article only when referring to something specific, so here the article is omitted.