Is that how you define a role play game? To me it is running around in a huge world leveling up by running into random baddies.
"...the characters would have to do different tasks for the story to continue."
Adventure Game^^^
Here are the major gaming categories
*Action (high-speed, lots of things to do)
*Adventure (story-driven, slower-paced, puzzles)
*Role Playing Game (personal character development, complex game structure, story-driven)
*First Person Shooter (From first person perpective, mainly-action, fast-paced)
*Sports (no need to explain)
*Racing (same as above)
*Puzzle (solving problems)
*Strategy (complex problems, decision-based)
*Simulation (simulates real life)
There can also be hybrids such as Action-Adventure.