Computer scientist here - NO that is NOT the prime function of an OS.
The prime function of an OS is to provide the appropriate abstractions to allow underlying and diverse hardware to be controlled in a consistent way, to provide task scheduling, memory management et al.
The interpretation of files is an application level concern - not an OS level concern.
Ditto for connecting to the Internet (or any other remote machine by any other mechanism - because there are others) and interpreting whatever data comes off it. (Whereas dealing with actually communicating with network devices on a low level is part of what an OS should do).
Since that is not what it says that's not what it is.
The basic technical argument is that it really isn't necessary that the HTML rendering engine of IE should provide functionality related to other core application level tasks when it really doesn't need to. Tying certain APIs together in a spaghetti of code is one of the anti-competitive practises Microsoft use in order to make it difficult to, say, drop the Gecko rendering engine in place of the Mosaic rendering engine (as is done in WINE to provide some sort of IE emulation).
That is the basic nature of the complaint.
ETA: And anybody arguing by analogy to other "bundling" practices of competitors fundamentally misses the point: MONOPOLIES ARE TREATED DIFFERENTLY. It is purposefully unfair because of the recognition that monopolies can be harmful to things such as innovation and improvement that we want to come out of captialism via the mechanism of competition. If Microsoft could not use their market position such that the vendor-lock-in tricks surrounding IE were not effective then no-one would care. They can, so people do care.
I'm sorry, but this is a nerd argument (no insult intended I'm Comp Sci and a nerd too).
The term "Operating System" has morphed from the days when it referred to the rather minimal system running on big iron. Your description of device abstraction, memory management, and tasking is the job of the
kernel. Try to find a linux consumer desktop distro that limits itself to that job. You get several shells (bash, csh, etc) giving you the
ls, pwd, etc., commands, you get an HTTP server, the X windowing system, a desktop or two (KDE, Gnome), probably a compiler or two, etc. We refer to those, collectively, as the operating system. Whatever we
call it, it makes sense to bundle those together for a typical consumer desktop. You'd make a rather different bundle for a server, for an embedded computer in your car, etc. But you'd choose those bundles based on the needs of the typical user. In any case,
no one (for reasonable values of "no one"

) sells only a kernel these days. (I've done a lot of embedded work, so I'm well aware of the exceptions to that. Heck, the embedded stuff I did didn't even have a kernel, but I digress).
Anyway, I view your argument as semantic. There are technical reasons for deciding what does and doesn't go in a kernel (the kernel of a media player is going to support file formats, the kernel of a automobile's cruise control isn't). But there are marketing and usability reasons for what gets bundled in an
Operating System, which these days means a kernel plus common sets of utilities.
VMS - more than a kernel
nextsep - more than a kernel
AmigaOS - more than a kernel (lots of multimedia and file handling built in)
SunOS - more than a kernel
Mac OS X - more than a kernel
BeOS - more than a kernel
I don't see why Microsoft should be restricted to only providing a kernel, or why anything beyond the kernel should be a competitor's IP.