What does the phrase "head down the rat's hole" mean here?

Question

Here is a heading of a game app's description:

"Head down the rat's hole"

The game lets you live the life of a rat that lives in a beautiful village. The player interacts with the rat's friends and make new discoveries about their lives.

Does the phrase "head down" mean "move" here? Like "move to the rat's hole"? Being a non-native speaker, I find it difficult to figure out its idiomatic connotation, if there is any.

The interesting thing is that there is no second occurrence of the word "hole" in the said description.

Answer 1

The phrase is a "take-off" ^{Definition: (1) (2)} or copy of a famous phrase:

Chapter 1.

Down the Rabbit Hole

--- Lewis Carroll, Alice's Adventures in Wonderland (also called Alice in Wonderland) ^{(3) (4)}

To "head down the rabbit hole," or "head down a rat's hole", simply means to go into it and downwards. (See definition)

The meaning of "go down the rabbit hole" is:

To enter into a situation or begin a process or journey that is particularly strange, problematic, difficult, complex, or chaotic, especially one that becomes increasingly so as it develops or unfolds. (An allusion to Alice's Adventures in Wonderland by Lewis Carroll.)
-- Farlex Dictionary of Idioms; Free Dictionary

or:

used for referring to a situation that is strange, confusing, or illogical, and often hard to escape from

Quoting from the people themselves is the easiest way of showing just how far down the rabbit hole we are going here.

Professor John Kennedy invites us to jump down the rabbit hole and imagine a world where U.S. Supreme Court justices are elected democratically.

Word story: From Alice’s Adventures in Wonderland, a famous children’s story by Lewis Carroll in which a girl called Alice falls down a rabbit hole into a strange dreamlike world.

--- Macmillan Dictionary

Answer 2

It's a bit of a funny one as I believe it's considered colloquial rather than "proper" English, but to head in [a direction] just means to go towards that direction.

A similar question has actually been asked in the English Language & Usage SE.

It's also worth noting that you can use it to mean a literal direction:

Headed down the street. (Travelling down the street)

Or metaphorical:

Profits had been down recently, but now they were heading in the right direction. (Profits had been down recently, but now they are increasing again.)

In your particular case, you have nearly interpreted perfection

"To head down the rat's hole" is just to go down it.

"Head towards" would mean move to it.

Answer 3

I'd say you were right on with your interpretation "move to the rat's hole": it is a common intro for video game/movie descriptions, to use a flowery version of:

Enter the world of [theme]

In this case, just a clever way to introduce the idea that you're going to be playing as a rat (enter the world of rats).

---

Along the lines of you could start a description of a Fallout game with:

Step out into post-apocalyptic Vegas... (enter the world after nuclear winter)

or a Harry Potter game might be described as:

Slip into the robes of a wizard... (putting on wizard's robes -> enter the world of wizards)