In lesson 5, starting with section 7 there are multiple exercises where one has to build sentences with possesive pronouns,
e.g.

li + gitaro => Tio estas lia gitaro.

For the plural questions, e.g. li + ideoj, it seems the correct answer is "Tio estas liaj ideoj."

I expected "tio" to have a plural ending, i.e. "tioj", like "*Those* are his ideas" in english.
Doesn't tioj exist?

What is tio, grammatically speaking? It seems like a "demonstrative pronoun" but it isn't listed as a pronoun in the grammar section.

It isn't listed as a pronoun, because...

The short answer is, that the -o suffix is always in singular(*).

For a longer answer let me explain from the beginning.

You have a bunch of prefixes (i-, ti-, ki-, ĉi and neni-), a bunch of suffixes (-o, -u, -a, -es, -e, -en, -el, -om, -al and -om) and you can combine any prefix with any suffix. The combinations are called la korelativoj (correlatives) or la tabelvortoj, because they form a nice table. Some of them are demonstrative pronouns in some languages, some particles, some... It all varies from one language to another.

As a side-note, one might argue, that -en shouldn't be part in the list above, since it is the accusative form of the ending -e. -e denotes a location and -en movement towards that location (cf. the preposition "en", esti en la ĉambro, iri en la ĉambron). I have found it easier to remember, when you list it among the others. YMMV.

The endings -u and -a can take both the plural -j and the accusative -n endings or both. These can be understood as demonstrative pronouns in many languages, and they require a main word, which they quantify or describe (individuo, individua aĵo, individua afero).

• ĉi tiu domo : this house
  
• ĉi tiuj domoj : these houses
  
• tiu domo : that house
  
• tiuj domoj : those houses
  
• ĉi tia domo : this kind of house
  
• ĉi tiaj domoj : these kinds of houses
  
• tia domo : that kind of house
  
• tiaj domoj : those kinds of houses
  
• ...

What does the suffix -o mean? It shows a thing (afero) by itself, Because there is no main word, you can't say, whether there is a single thing or many. This is perhaps more obvious in questions:

• What is there? : Kio estas tie? (cf. English, you don't ask: What are there?)

The expression Tio estas liaj ideoj follows that principle. The problem is, that in many languages (my native included) much can be derived from the context (subkomprenita). For instance sentences Li havas multajn gitarojn, Ĉi tiuj estas akustikaj. are understood by many, that the guitars are at least in two groups, and those in the group closest to you are acoustic. Therefore I would say Tiuj estas liaj ideoj.

*: I vaguely remember having read about a case in discussion of sets of sets, where you can (must?) use forms like tioj, but it was on so high level, that I didn't understand it.

Tio (that thing) is abstract, tiu (that thing) is concrete.

The thing is I haven't got the money, I haven't got the time, and I don't want to do it anyway.

You wouldn't say the things are ... However Are these your things?