Well, it really depends on what you mean by a "web" server.
If you mean a piece of software that implements the protocols typically used for (the server aspects of) web browsing, such as HTTP, TLS, OCSP, and so on, then what's important is what the software does, not whether or not it is accessible from any given system.
If you mean such a piece of software that is also accessible from some system, which may or may not be a different one from the one where the software is installed, then you must also define the boundaries of such access. Is it acceptable for it to only be accessible from the local system, or from the local network, or from some other known network, or from anywhere on the Internet? What about a system that hosts "web" content, using TCP/IP, but which has no Internet connectivity at all?
There is also the matter of that the software may be running on a system other than that on which it is installed.
For simplicity, one usually talks about software by function, not by boundaries of access. So, say, Microsoft Excel is a spreadsheet application; this doesn't change based on whether or not you can access a given copy of it from some given computer. Similarly, a program that is meant to implement web server functionality will usually be referred to as a web server, regardless of whether it's actually doing the work of serving web content to some particular system at some particular moment in time.
By that definition, the Apache web server implementation is a web server regardless of whether it's accessible from somewhere else or not.
And that's all software. One can also argue about whether a specific computer is a "web server" or not. At this point, one usually considers a computer's primary useful purpose, because a single computer, even one primarily used as a web server, will still run a lot of other things. By that definition, a computer would be a web server if one of its primary functions is to serve web content.
And that's a whole computer. One can also argue about whether a specific instance inside a virtualized or containerized environment is a "web server" or not, irrespective of the greater purpose of the host system.
And that's still a single computer. Pretty much the same argument can be made about virtualization clusters.
And on it goes. It's
turtles chips all the way down.
If you want to disambiguate, then instead of trying to come up with a single word or even a single term, rather specify what you really mean. "An installation of the Apache web server software where the host has no Internet connectivity" is more verbose, but it's also fairly unambiguous. "A physical computer with the primary purpose of serving web content to locally connected clients" is also fairly unambiguous. Both can be abbreviated to "a web server", and the intended meaning is often clear from context, but if it really matters, just say what it actually is.