I think people who haven't worked in/around IBM struggle to comprehend the sheer number of products and services it actively supports and only a portion of that are mainframe products. There are many products that have 100+ engineers on them but might never even make common conversation for how specialized they are. Additionally IBM has a high headcount for supporting those products, with 24/7/365 phone/hands-on support so that can sometimes be almost the similar number of people as the engineers actually developing the product. Since the products are so specialized there are specialized support groups per product. It's definitely easy to have 150+ people per product (especially from the heavy acquisition style they had been doing pre-Red Hat) so the numbers quickly adding up. Many of these groups have enough organization to transition to a standalone company's product team if they could replace the HR, accounting, and other company pieces.

There is certainly also consulting and other groups of people too, but they were not the majority.