They (id tech 2-4+) definitely are considered full on world class engines, FPS specific but still. They each have a renderer, physics, scripting, asset pipeline

They (id tech 2-4+) definitely are considered full on world class engines, FPS specific but still. They each have a renderer, physics, scripting, asset pipeline, map and data formats, tooling, etc. and were used to make other games. They are too big, unified, oppressive (as in - they control the main loop, their elements are all together, you can't mix and match easily, your game code is on a level of a plugin for the engine code to call, not the other way around) and multi domain to be considered libraries/frameworks.