Sure,
Well, according to the link it turns out that there's no subfolder hierarchy in the Tie Fighter zip file. Luckily, I had X-Wing Vs. Tie Fighter installed on my machine and I was able to recreate the different subfolders based on that.
Once I had the game running, it would crash when looking for specific files. I would then get the particular files the error message mentioned, create the subfolder in question and simply cut and paste.
The subfolders are as follows: CP, RESOURCE, SOUND, MISSION, FRONTRES and IVFILES.
((Keep in mind that some of these folders might not be needed as they relate only to XvsTie. I've also duplicated a large number of the files to be on the safe side))
The MISSION folder contains the *.TIE files
FRONTRES and IVFILES contain the *.LST files (I'm not sure the IVFILES folder is needed at all...)
For the RESOURCE subfolder I copied the entire root into it.
SOUND contains the *.ENG, *.WDR and TESTMIDI and TESTWAVE
And CP contains the *.INT, *.LFD and *.PNL files.
Tada!
If it ain't broke, fix it till it is.