I sadly never got to play the original even though it was on Genesis and I think SNES. I wanted to though as I think it had graphic adventure elements and that is my fave genre of game. The one that came out a few years ago was a straight up FPS, this looks different again. Does it have graphic adventure elements again?
Well, the SEGA Genesis
Shadowrun versions are actually two completely different games. The Genesis version was (sort of) an open world RPG. There was a story but most of the gameplay is actually spent completing random runs to get enough nuyen (money) and karma (exp) so that you are strong enough to advance in the main storyline. The were also a SEGA / MEGA CD Shadowrun which unfortunately never left Japan (apparently some people are working on a fan translation). The SNES version was a more linear RPG, but had many of the adventure game elements you were talking about.
Shadowrun Returns is different, but it definitely will take inspiration from both of the 16-bit games (it even takes place in between both games; 4 years after the SNES game and 4 years before the Genesis game). You don't need to play those games before this one, but there will be references to them. On Steam the genres listed for the game are actually "Adventure, RPG, & Strategy". The combat will be a turn-based tactical system (very similar to the combat in X-Com: Enemy Unknown w/ cover). And you will of course be able to upgrade your character with cyberware, new weapons, or magic spells. Outside of combat, there will be lots of conversations with multiple options, many of which take into account your character's stats such as Charisma and Ettiquette w/ various factions). Very often there will be multiple ways to complete a missions such as acquiring a disguise or using stealth to sneak past guards, intimidating or bluffing your way past the guards, or simply taking them down with brute force. And Deckers can hack into the security system to disable alarms / cameras, open locked doors, etc. The main storyline will involve investigating the murder of your childhood friend, which is probably where the adventure game aspect really comes in. They've mentioned in the alpha video that often there will be objects in the environment that you use (such as a computer terminal to get information).
But what really makes the game for me is that it is going to include a game editor (similar to the toolset for Neverwinter Nights) that will allow players to make their own adventures. So we can expect a wide range of player generated campaigns; probably ranging from very combat heavy missions to more role-playing / adventure oriented campaigns with little or no combat. (If it's anything like NWN, there will be some awful stuff, but also some really incredible stuff that may even be better than the official campaign).
Edit: They just posted an update showing lots of portraits and how the first page of the character generation screen will look: http://harebrained-schemes.com/post/chris-dev-diary-characters/