As Jlawler stated in his comment, the that in the sentence in the question is a singular distal demonstrative pronoun.
a. Ginny likes that.
It is a pronoun because it appears where a noun would often appear, e.g. Ginny likes cake, and because its content, i.e. what it refers to, is available in context.
One can note in addition that the word that functions in a number of other ways, in addition to being a demonstrative determiner or demonstrative pronoun. It can also be a demonstrative adverb, e.g. It was that controversial. Perhaps its most common use in English is as a subordinator (i.e. a subordinate conjunction), e.g. They said that it was finished. And yet another use of that is as a relative pronoun, e.g. The people that were present were hungry, although its status in such cases (i.e. whether it is indeed a relative pronoun or not) is a matter of debate. Here is a list of its uses:
demonstrative determiner: Ginny likes that cake.
demonstrative pronoun: Ginny likes that.
demonstrative adverb: Ginny is that hungry.
subordinator (i.e. subordinate conjunction): Ginny said that she likes the cake.
relative pronoun (controversial): The cake that Ginny likes is chocolate.