From what I experienced, you do not have to complete the first game to play the second. Each game has their own shortcut on the desktop, so you can play the first or second game whenever you want to.
So I would say this IS the gold edition.
That is not the Special Edition then, the Special Edition is a Windows 95 game and does NOT work in DOS, it definitely includes every level from both EWJ 1 and 2 in a single program.
Edit 2: Title screen: http://i.ytimg.com/vi/fQ92DFIP1Wo/hqdefault.jpg
and picture of the Special Edition game running on Windows without DOSBox or DOS (Shows the level select list too) http://i.ytimg.com/vi/Zcvd3bgOH34/maxresdefault.jpg
Edit 3: For information on how to play the Windows 95 version under a modern operating system, check here: http://www.play-old-pc-games.com/2014/09/07/earthworm-special-edition
/ (Doesn't include download link to pirated copy of game, just fyi for you moderators, only information on getting the game to work)
Earthworm Jim for Windows 95 is a direct port of the popular Sega CD version using the Exodus Video Gaming Technologies created by Kinesoft Development. The technology consists of highly optimized programming libraries that allow for the conversion of console games to Windows 95 primarily using 486 assembly code for the main game logic and C++ for the shell... blah, blah, blah. Okay, enough of the technobabble. Here's the story. Activision wanted to make some really cool games for Windows 95 because... well, there have never been any cool 2D side-scrolling action games for Windows. So, because the guys at Microsoft made Windows 95 a gaming platform in addition to an operating system, Activision hired this company in Chicago called Kinesoft Development, who had just developed this really great technology for porting console games to Windows 95. Still raking in the dough for its popular game Pitfall: The Mayan Adventure, Activision then released a Windows 95 version that was not only able to fully capture the speed and gameplay of the original but contained lots of enhancements. So, after seeing what could be done in the new operating system, Activision called their buddies at Shiny Entertainment and licensed the rights to do a Windows 95 version of Earthworm Jim... which accounts for why you are reading this now. Anyway, like Pitfall, all of the speed, gameplay and fun of the original has been captured AND a bunch of enhancments have been added to make your gaming experience more pleasurable. So, on behalf of Activision, Kinesoft and Shiny... HAVE FUN!
-- 256 color graphics! The backgrounds and animations have been painstakingly updated from 64 to 256 colors. That's a whopping 192 extra colors that provide for PC-quality graphics!
-- CD-quality music! The game features a CD-quality soundtrack that contains over 50 minutes of cool music by the guys at Tommy Tallarico Studios. You can even listen to the music on your standard CD player. So, do Tommy a favor and pop in the Earthworm Jim CD whenever you go cruising down your local boulevard.
-- A new weapon! Help Jim blast his way through all of the levels using a new homing rocket not included in the cartridge versions.
-- A new level! Manuever Jim through an entire new level complete with new enemies and hidden goodies not included in the cartridge versions.
An Earthworm Jim Desktop Theme! Customize your Windows 95 desktop with this really cool Microsoft Plus! desktop theme that was created by the ever-productive Tin Guerrero. Now you can install Earthworm Jim animating cursors, sounds, icons and wallpaper... which will automatically make your computer better than anyone else's.