I think the biggest dividing factor of Risen and Gothic 1 to 3 (as they're made by the same company. Not Gothic 4 or Arcania though) is the combat and whether you like it or not.
The combat is real time with a focus on blocking, dodging and hitting when the enemy is vulnerable. If you go in swinging your sword willy-nilly you will get killed quickly. Another big part of combat is training. As you put training points into, say, Sword skills you will become faster at swinging and be able to pull off combo moves (three hits instead of one type things). Magic is part of your available skills but in all the games I mentioned it is very much an investment that pays off later in the game.
From what I remember of Risen, it plays very much like Gothic 1-3. I cannot comment on 2 or 3 as I have not played them.
As for the story, I think Risen is about ancient things being awoken, I haven't finished it.
This may be a little confusing. Because Gothic 1-3 was made by Piranha Bytes as well as the Risen series, Risen pretty much continues the story of Gothic 1-3 despite it not being set in the same world or having the same characters. Due to Piranha Bytes not having the rights to the world of Gothic, Risen is a lawyer friendly expy of the Gothic 1-3 world. Due to this it may be worth your time playing through Gothic 1, 2 and 3 but it is by no means necessary. The plots don't have too much connection between games but it fills out the backgrounds of characters and the world.