No, every level is not made up of pages.
The page level is one contextual level at which you can deal with content, but your information (and knowledge) hierarchy may contain levels at finer or coarser levels than the page, and may in fact not even include the page if it's not relevant to the scenario in question.
For example - the structure may include areas above the page - such as general topics, collections, knowledge bases, and other broad information domains. Or it may include sub-page areas which connect together like lego to make the page itself.
In particular with displays being so diverse in size, it's very important to think about content at the sub-page level in order to determine priority, relative location, dimensions and copy/microcopy depending on the available resources.
As Eliel Saarinen said:
Always design a thing by considering it in its next larger context - a
chair in a room, a room in a house, a house in an environment, an
environment in a city plan.
And that very much applies to information architecture, content strategy and many other ux disciplines.
As a consumer of information, you do typically see pages because that's how your browser or screen appears to present the information, but behind the scenes, that is not how the information is really organized. Much thought goes into content organisation and how entities are linked together.
Consider a book - a real one! It has pages, sure. But it has sections and chapters and indices and appendices and paragraphs and sentences and words and footnotes... It has an author who's written other books and a publisher who has many authors... The page-level is just one layer in that structure at which you can design for.
Finally, Lee McIvor gave an interesting talk on the art and science of UX and responsive design at UX Cambridge recently in which he said of one large project that he had learned 3 things:
Putting the question into context
Looking at the statement:
you should group and structure information at the page level
This has been somewhat taken out of its context - ironically!
The phrase comes from Morville & Rosenfeld's classic book 'Information Architecture for the World Wide Web' when it's talking about how not to overwhelm the user with information and how to balance depth and breadth of navigational hierarchy.
It goes on to describe the website of the National Cancer Institute (US) below, as a well tested example.
The advice is not saying that you should take the information and "structure it at the page level". It is saying that at the page level, you should group and structure the information. Period. This is in order to chunk the information into manageable amounts.
That is equivalent to the "designing small interactions" from above. Each area on the page is carefully cultured for optimal use, but you could equally well extract and re-use these small components elsewhere.
By grouping the content into separate areas, and structuring it in a sensible fashion (on each page) you make that page more easily digestible, whether it's types of cancer, resources, news, statistics, or cancer topics, finding a cancer type, etc.
i.e. At the page level, it is grouped and structured.