If the file had a Stuffit extension it was most likely created on a Mac since Stuffit is like Zip but for Mac computers. It would have an .SIT extension. Like a ZIP file it must be unstuffed. Since Mac files are often saved without extensions, it is entirely possible that someone along the way thought all they had to do was to rename the file with an EPS extension and it would magically become an EPS. Or it is possible you are dealing with an EPS generated in Photoshop which is a whole different flavor of EPS.
To take a different approach, try:
1. Opening the file in a text editor and see if there is anything that resembles an English plain text header. Even if not, there may be some clues there as to what program saved the file.
2. Opening the file in Photoshop. If it's a Photoshop EPS it may just be recognized.
3. Changing the extension to some common image formats like JPG and TIF to see if that makes them recognizable.
here is an example of the first eight lines of an Illustrator EPS file:
%!PS-Adobe-3.0 EPSF-3.0
%%Creator: Adobe Illustrator(TM) 3.2
%%AI8_CreatorVersion: 8
%%For: (Fred Weiss) (Allied Computer Graphics, Inc.)
%%Title: (acg00219_Baseball_Pitcher.eps)
%%CreationDate: (1/21/2006) (12:08 PM)
%%BoundingBox: 184 124 429 628
%%DocumentProcessColors: Black
By contrast, an EPS saved from Photoshop is in code until you get to the fifth line where it says:
Adobe Photoshop CS2 Windows