FPS style you are referencing:
Doom- linear campaign
Halo- linear campaign
CoD- linear campaign
BF- linear campaign
RPGs
Skyrim- nonlinear
Borderlands- nonlinear
Final fantasy- nonlinear
Mass effect- nonlinear
Etc
Destiny is not linear and thus does not fit into the categories with the other traditional "FPS". It has dungeons and raids which are not items found outside the RPG genre. It's pretty obviously just an RPG that happens to be from the FPS perspective. As I stated in my first comment, it's the style not the genre
English
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No, Destiny is WAY more a FPS than a RPG or anything else. It's like Halo with single Missions besides the linear main story you can also play cooperatively. In the end you're just shooting stuff from First Person View without any thought of the role you are playing...because you literally have no role to play. Hell, eben the Masterchief is more a role you can identify yourself with than any nonamed guardian.