Emacs is an ok lisp machine. It is much better than many common lisp distributions which are typically not very good lisp machines (I believe the proprietary systems are better in this regard).
Clinging on to Emacs as a lisp machine can mean clinging onto the more dynamic customisable extensible computation environment epitomised by the lisp machine, and in this sense I think it is more understandable
GNU Emacs is an extensible text editor, but not a Lisp Machine. A Lisp machine is a computer with a Lisp OS on the metal. This means the OS itself is written in Lisp and not just some specialized application, interfacing to a foreign underlying OS. A Lisp OS has also an open GUI and not just an editor-buffer-based UI.
With GNU Emacs the extensibility ends when one calls an OS tool or an OS library - for a Lisp Machine there is no such distinction.
GNU Emacs is a mostly single-threaded editor, with a horrible user interface and heroic efforts from users to deal with thousands of modes and keystroke combinations.
None of the extensible Lisp applications are 'Lisp Machines': not Autocad, not Audacity, not iCAD, not Creo Elements, not GNU Emacs, not OpusModus, not Macsyma, ... They are Lisp applications which expose a development interface and a development environment (yes, Autocad has Lisp development tools) and users are writing complex applications on top of those.
On a real Lisp Machine, an Emacs-like text editor is just one application and one interface style.