Me gusta / a mí me gusta

[Tina]

I'm confused about when the 'a' is needed. Some examples in my book:

Me gusta el cine.
Me gusta tocar la guitarra.
No me gusta.

A mí me gustan los deportes.
A mí también. ¿Y a ti, Maria?
A mí no.

The book only says this:

The context may make it clear who you are referring to, but if it doesn't, you can be more specific by using the following construction with the preposition 'a' with exactly the same meaning as above.

I don't understand what this means. The context looks the same to me in both instances. The person is stating that they like something or they don't. Can someone help me understand?

[Rusty]

You are right, the context is clear in these examples.
The preposition 'a' introduces a prepositional phrase and, in this case, the prepositional phrase is the indirect object.

The verb gustar takes an indirect object. The indirect object names the person to whom the subject is pleasing. When only the indirect object pronoun is used, the indirect object may also need to be expressed if meaning is unclear OR if emphasis is desired.

In the case your book cites, the indirect object is adding emphasis because the indirect object pronoun is clearly referencing a particular person (the first person).

Me = to me (indirect object pronoun)
gusta = is pleasing (verb)
el cine = the cinema (subject)

a mí = to me (indirect object)

Do you see the redundancy? Both 'a mí' and 'me' represent the exact same person. The first is an indirect object (a prepositional phrase acting as the indirect object) and the second is an indirect object pronoun.

So, emphasis is the only difference between 'a mí me' and 'me'.

[Tina]

Thank you Rusty. I'm still trying to grasp the difference. So is either way correct?

[Rusty]

Either way is correct, yes, but adding emphasis isn't always done. In other words, you don't want to use the emphatic form if you're not truly trying to add emphasis.

In English:

I like playing the guitar.
I like playing the guitar.

The second sentence is the emphatic form of the first sentence-the boldface type indicating where the speaker dwells on the word 'I'. The speaker wants the listener to focus on the pronoun 'I', as if to avoid/correct some kind of misunderstanding.

In Spanish,
Me gusta tocar la guitarra.
A mí me gusta tocar la guitarra.

The second sentence is the emphatic form of the first. I didn't write 'a mí' in boldface type because the indirect object is not said (dwelt on) like the English emphatic form.


NOTE: I should add that I have only been commenting on the text you quoted from the book (not the sentences) and what appears in the thread's title.
Only one of the sentences you posted actually applies to what I've gone on about (emphasis). It's the first sentence that begins the second dialog (about sports). No other sentence applies to text you quoted from the book (about context).
The last two sentences are examples of where established words ("like sports") have been omitted. In these, the prepositional phrase (acting as an indirect object) is used where the indirect object pronoun cannot be used (because the verb is omitted).
By the way, the usage of the indirect object in these sentences is because the verb takes an indirect object. With other verbs, like 'tocar', the dialog with omitted verb and direct object would be very different.

Toco la guitarra.
Yo también. ¿Y tú, Maria?
Yo no.