I was finally able to execute this file and find out its contents. It
is a patch to DirectX Media Runtime 6.0, a part of the MicroSoft
DirectX system. It contains three files...amstream.dll (version
6.00.02.1104, danim.dll (version 6.00.04.1116), and p_981116.inf. The
two library files go into the WINDOWS/SYSTEM folder, while the .inf
goes into the WINDOWS/INF folder. It will only install to an
un-patched version of the Runtime. I was able to make it execute by
installing Win95B, which contains DirectX 2 (4.03.00.1096), then
installing the 6.0 Runtime (Enduser.exe, downloaded from MicroSoft),
and then the p_981116 patch.

For some reason, some installers (like for my Logitech QuickCam
Traveler v5.4.3) write this file to the registry "RUN" section to
execute in quiet mode and to not display anything on the screen
(p_981116.exe /Q:A) at each bootup. Once the files are installed,
there is no reason to keep executing this, so it may be deleted from
the registry with no concequence. Leaving it there just wastes bootup
time as it tries to install over and over again. It was not a
self-deleting file/installer, or a "RUNONCE", although it probably
should have been.

This patch was superceeded by the p_9904.exe patch and will not
execute if it has been installed (I guess it checks the versions of
the replaced files, so it is a "smart" installer, and another reason
you can delete it from the registry). p_9904 contains the files
amstream.dll (version 6.00.02.1104), danim.dll, dxtrans.dll,
dxtmsft.dll, dxtmsft3.dll, datime.dll (all are version 6.01.09.0727)
and p_9904.inf. Note that the amstream.dll is the same in both
patches, but the danim.dll was updated in the p_9904 patch.

For some reason for me, when I executed the p_981116 patch, it ran but
it didn't install (even though it appeared to). To actually make it
install, I had to manually extract the files using the "RUN" command
(p_981116.exe /c /t:C:\temp ...which extracts the files to the
directory "C:\temp"), and then right-click on the .inf file and select
"INSTALL". Only then did the files properly install to the system. The
p_9904 patch did not have this problem.

All of this is just history, since with later versions of DirectX,
these files are all replaced/updated anyway. But I though I'd post
this here, so that all whose questions were unanswered (including my
own), now have an answer.