Your definition from websters is called "the essential meaning" and is literally not the dictionary definition. It is very similar to using definitions from what google returns at the top of a search page - kind of useful but not the same as the definition of the word.

Look below that in the next section. There you will find the definition of bureaucracy. That section is called "Full Definition of bureaucracy"

  1a: a body of nonelected government officials
  b: an administrative policy-making group
  2: government characterized by specialization of functions,
  adherence to fixed rules, and a hierarchy of authority
  3: a system of administration marked by officialism, red
  tape, and proliferation