Relax, it's all a matter of opinion.
I for one don't believe in the category of RPGs. Just because you get stronger and edit stats, does it make it an RPG? Then some racing games would be considered RPGs. I happen to classify games on what they majority of the game is, since some games have more than one gametype.
Puzzle games are games that focus on decisions. It could be memorizing a certain sequence of a song or finding which key goes where. Pure puzzle games don't have a time limit. Zelda is mainly a puzzle game because most of the time, you are in dungeons, which have infernally difficult puzzles.
Reflex games involve doing the right manuevers at the right time. DDR would fit into this category, since you need to press the button as it's highlighted. Most racing games would fit into this category, since you need to use reflexes when steering your car.
Action games are just that, action. These involve grueling combat, which is usually mindless. Some good examples? Resident Evil 4 has you mowing hordes of mutated people. Gauntlet Legends has you hacking monsters here and there. Dynasty Warriors pits you against armies. I totally despise a game that only has pure action in it, since it gets EXTREMELY repetitive.
Strategy games are the games that I enjoy the most. Some fighting games fit this category like Soul Calibur II. If your friend keeps doing a certain move, you can ADAPT and use a move that's designed to counter it. The adapting part is why it's called strategy. Games like Warcraft and Starcraft have you ADAPTING to your opponenent's weaknesses. The evolving gameplay allows enormous replay value. The main difference between puzzle and strategy games is that puzzle games have a llimited number of solutions, while strategy games has the puzzles, whether it's an enemy or the environment, changing.
Great plots have nothing to do with gameplay. If the game has a superb plot, then that makes the game that much better. In fact, I buy games if they have detailed and intriguing storylines.
So now onto my version of this thread...
REFLEX:
It never gets repetitive because humans never play the same. The amount of skill, luck and teamwork seems to be balanced. However, I'd prefer if they made it more realistic such as using ironsights and removing the HUD.
PUZZLE:
This a PURE puzzle game. You are given the situation and you must figure it out. Unlike other games, there is no time limit; it's a game of patience and knowledge.
ACTION:
As I said before, I loathe action games. HOWEVER, the multiplayer in this game is a pleasure because of the amount of teamwork that is needed to succeed. Then the art style, graphics and decent plot round the package off.
STRATEGY:
You might denounce it JUST because it's a card game, but it really deserves a second chance. I love the fact that you are given the choice to choose HOW you want to play the game from 300 cards. This game is strategic because there is no time limit and it's all about choosing the right decision and a bit of luck.
PLOT:
It was hard deciding between this or Eternal Darkness. Eternal Darkness had a more detailed story with a great narrative, but lacked a climax. Second Sight has great character development, a good variety of gameplay and a great plot twist, even though I missed it the first time. The endings of both games are the typical good guys win, but at least they both had great characters and decent logic.