The term 'mainframe' helped to categorize the physical aspect of
machines from the 1950s through 1980s , but since then it has
diminished as a differentiator.
The mainframe architecture which emphasized dedicated processors to
handle IO, front-end processors, support for large numbers of diverse
peripheral devices, OSes which included batch and interactive
services, also appears to help categorize machines into the 1980s.
After that these combination of features started to appear in new
systems or were added as extensions to so-called midrange systems (not
only IBM), increasingly on lower cost systems.
The distinctive mainframe 'style' of computing: the way of interacting
with the operating system, OS design, communication protocols, legacy
support - captures systems onwards beyond the 1980s till present day.
This includes desktop (PC), small deskside cabinet implementations of
mainframes like IBM XT/370, P/390, Unisys SCAMP (A-series, Unisys
System 80), but also the newer (current day) technology
implementations like the z-Series and the Unisys Libra. This criteria
helps to answer the question: "What type of computing is a P/390 or
Hercules Simulator showing? Answer: a mainframe style of computing, it
is not a physical mainframe, but the manifestation shown is a
mainframe.'.
The marketing folks latched onto the mainframe term as a way to garner
some of the halo effect of big, powerful, expensive ("THIS product is
just as good as a mainframe but cheaper" etc),
meet-the-needs-of-any-business mantra which sold them so well through
the early decades. I think at various times marketeers tied themselves
into knots trying to reconcile the categories. Unisys advertised the
A1 as a "small-frame" computer in the late 1980s.
Therefore mainframe only exists today as a identifiable category
because examples of the legacy architecture (although significantly
updated in technology and implementation) continue to exist. If the
mainframe products of IBM and Unisys [*] disappeared tomorrow, the
idea of mainframe (as we collectively know them) would fade too.
[*] I expect there are other manufacturers, I am using IBM and Unisys
as just two examples.