As marketing people start to think more about making games and gamifying things, it's probably a good idea to understand what makes something a game and what doesn't.
Simulators (Examples: Flight Simulator, Sim City, Dwarf Fortress) -- A simulator is a type of interactive system whose primary responsibility it is to simulatesomething.
In the end, one of the interesting differences between a simulator and a game is that it's not a valid complaint to say that a simulator isn't fun. Simulators really have no inherent requirement to be fun -- they only need to simulate something.
To be more precise, the real difference between a simulator and a game is that a simulator is not a type of contest, and a game is. Of course, I suppose you could have a "contest simulator", but the fact remains that competition is not an inherent part of simulation.
Contests (Examples: a weightlifting contest, Guitar Hero, Simon) -- All games are contests, but not all contests are games. The issue is that while contests are competitive, they do not require meaningful decisions. They are often a pure measurement of ability -- a simple question of "how much weight can you lift", or for the example of Guitar Hero or Simon, "how well have you memorized this sequence". It can be a bit hazy in some situations, but generally I think most of us have a pretty good innate sense of what the difference is between a game and a contest.
Puzzles (Examples: a Portal level, a jigsaw puzzle, a math problem) -- A puzzle is another word for "a problem". A puzzle has a single correct answer -- a "solution".
Some games can also be solved ("complete information" games, such as chess, where all the information about the game state is known to the player), however if it is common for people to be able to solve a game, it's considered a knock against that game (Tic-Tac-Toe is solved easily by most people other than very young children, and therefore it is not considered a good game for adults). Puzzles, on the other hand, do not get a knock for having a solution; that's what they're all about.
So do puzzles have "decision-making"? I argue that they do not -- at least, certainly not at all in the same way that games do. Puzzles are not games, because while some puzzles allow players to make decisions, this is actually rather irrelevant to the outcome. All that matters for a puzzle is whether or not the player gave the correct answer.
If all of that is confusing, here's a helpful chart: