What is a special-purpose computer that functions as a component in a larger product?

Do you mean what type of computer is a special purpose computer [...]? I'm not aware of any single term for a computer that functions as a component in a larger system.

Below is some examples of computers which do function as a component in larger systems:

Clustering Operating System is a type of software which allows multiple computers to join together and its software + networking disguises the underlying computers to look like one large computer.

This is useful for scientific computing where all computers will be guaranteed to not shut down, but more resources than is available on one computer is needed to complete the computation.

Fail-Over Load-Balancing Server is another type of computer. It's purpose is to run a process on multiple computers at once. And the one that succeeds first is the one that gets processed. The Load-Balancing part knows what computers to start a process on. This is so if one computer goes down, the software component will still get ran.

This is useful for web-servers which need fault tolerance so if one computer goes down, the software still performs its job.

There are also Industrial Computers which function together, but individually, to produce a single product. Like on conveyer belts in a manufacturing plant.