I'm not a labor historian specifically, and I don't know of any other surviving examples of "company songbooks" from the mid-20th century. However, I see in this artifact a intersection of two trends in mid-20th-century American corporate culture: opposition to unions and generous benefit packages.

There was an effort during the early to middle parts of the 20th century for large companies to try to provide a wide variety of fringe benefits for their employees like in-house baseball leagues and theater troupes. These were both a fringe benefit to retain workers, but also were been by management as a relatively cheap way to encourage good feelings towards the company and thus prevent the type of worker discontent that might create a fertile ground for union organizing.

At the same time, we shouldn't dismiss this entirely as a tool of corporate overlordship. Employees had agency, and they seem to have enjoyed their company-sponsored leisure activities as a cheap way to have a good time on the boss's dime. Lizabeth Cohen discusses these "company leagues" in her book Making a New Deal: Industrial Workers in Chicago, 1919-1939.

The songbook you linked to also looks like some other corporate ephemera I've seen related to the production of so-called "industrial musicals" in 20th-century Detroit. While they eventually became more of an advertising vehicle later in the 1950s and 1960s, industrial musicals originated as a form of entertainment for the workers, who generally were both the audience and the performers. In the early days it wasn't uncommon for there to be dialog that gently (or not so gently) poked fun at management or even particular persons around the factory. The closest 21st-century equivalent is probably the little skits people sometimes put on at office holiday parties.

Another similarity I see is that the lyrics from many of the IBM songs look almost like parodies of popular union songs of approximately the same era. I wonder if the whole thing wasn't part of some kind of anti-union push by the executives.

To follow up on /u/AshkenazeeYankee 's answer. These programs, including recreational activities, as well as housing, financial assistance, health programs, etc., is what’s now referred to as “welfare capitalism.” A lot of the motivation was, as /u/AshkenazeeYankee says, to discourage labor unions, but the desire for a stable, happy workforce also played a part [1, 2, 3].

For an example of this in the 1920-1930 time frame, look at Western Electric’s Hawthorne Works outside of Chicago. Savings, insurance and pension plans, health lectures, first aid classes, as well as:

…a program of recreational, social and athletic activities. All these activities were conducted by an employees’ organization known as the Hawthorne Club. All employees belonged to this organization. They elected their own officers and promoted a wide variety of activities ranging from motion picture productions to track meets, and from target practice to checker tournaments. Gymnastics and athletic sports were conducted in a gymnasium and on an athletic field. Entertainments of all sorts – bands, orchestra, glee club, prominent speakers, dancing – were on the calendar during the noon and evening programs. An evening school, with over 3,000 students in attendance, receiving instruction in 45 different subjects, was conducted by this club. [4, p. 10]

[1] Gillespie, R. (1991). Manufacturing knowledge: A history of the Hawthorne experiments. Cambridge: Cambridge University Press.

[2] Kessler-Harris, A. (1982). Out to work: A history of wage-earning women in the United States. New York: Oxford University Press.

[3] Wren, D.A. (1994), The History of Management Thought, 4th ed., New York: John Wiley & Sons.

[4] Roethlisberger, F. J. (1939). Management and the worker: An account of a research program conducted by the Western Electric Company, Hawthorne Works, Chicago. Cambridge, MA: Harvard University Press.

PS to /u/AshkenazeeYankee -- thanks for the reference to Cohen -- just what I need for a paper I'm currently working on.