> DOS barely has any concept of processes

That's not true - DOS lacks multitasking but it absolutely has a concept of processes. They're called PSPs (program segment prefixes, a struct containing data about that process) and the OS has a range of syscalls to manage them. Any program can spawn a child program and wait for its completion.

The memory allocation syscalls track which program owns each dynamically allocated block of memory (the block has a header which points to the PSP), and frees the blocks allocated by a program when it exits. The filesystem syscalls deal with file handles opened by processes in just the same way.

The famous "terminate and stay resident" syscall causes a program to exit and return to its parent process while keeping its PSP and dynamically allocated memory blocks intact.

16 bit Windows introduced multitasking but reused DOS's PSP based process model and would allocate a PSP for each Windows task, switching the current DOS PSP when switching between Windows tasks.