"Modular" is a very confusing word to use in the title, since IBM's earlier computers were made from modules. IBM even called the cards in its 1950s-1960 computers "Standard Modular System" (SMS) cards.
I think what "modular" is alluding to in the title is that the 360 introduced a whole line of compatible computers, rather than making each computer a separate architecture as had been previous practice.
In other words, the 1959 IBM 1401 was modular in the sense of being made from modules, but it wasn't modular in the sense of being part of a product line. (The improved 1410 was only sort of compatible.)
Did they perhaps mean "modular" in the sense of the computer being composed out of a set of standardized modules, with none of the modules having been constructed for that computer alone?
Not just component-wise upgradability or ease of assembly, but rather eliminating entirely the concept of doing one-off "integrations" to create new products in the line. In other words, doing with their computer parts what IKEA does with furniture parts: designing and manufacturing only at the component level, then feeding all the finished components into a shared pool of resources, where products are then simple assemblies of resources from the pool.
I'm a bit late to reply, but the idea of IBM's modular SMS cards (1950s-1960s) was that they would create a relatively small number of these cards and would build computers out of them. (A card might have a few AND gates for instance.) In practice, new machines required custom cards and IBM ended up producing thousands of different SMS cards. So the idea was only semi-successful.
I think what "modular" is alluding to in the title is that the 360 introduced a whole line of compatible computers, rather than making each computer a separate architecture as had been previous practice.
In other words, the 1959 IBM 1401 was modular in the sense of being made from modules, but it wasn't modular in the sense of being part of a product line. (The improved 1410 was only sort of compatible.)
SMS link: https://en.wikipedia.org/wiki/IBM_Standard_Modular_System