The solution was to close the pipe handles after creating the process.

So

  if (!CreateProcess( 
    NULL,
    filename, //TODO: check unicode?
    NULL,
    NULL,
    TRUE,
    0,
    NULL,
    NULL,
    &si,
    pi)
  ) {
    printf("Could not create process\n");
    return NULL;
  }
CloseHandle(g_hChildStd_OUT_Wr); 
CloseHandle(g_hChildStd_IN_Rd);

I guess because then only the child holds a handle to the resources, not the parent.