If I had to distill down what makes a game fun and engaging for me - and what people have told me is fun about my games - it really boils down to two concepts that I try to always keep present in my games. Those concepts: Player Agency and Consequences.
Player Agency means that the players have the ability to influence the game. There is not a set, locked path that they are on. If they want to go left, they can go left. I - the GM - am not going to force encounters, force actions, or force story points. The players have control of their characters, and the story is focused on those characters.
Consequences means that the choices the PCs have carry weight. Their decisions will be reacted to by the world. Inaction as well as action can have consequences. These consequences can be good, bad, or mixed depending on the situation.
Combined you have a game that is focused on the PCs. The players choose what they do and how they do it. The world reacts to the PCs and the game progresses from there. Easy peasy, at least in concept.
A game with these has the following cycle of play:
- The GM presents the situation/sets the scene
- The players say what they do/how they react
- The GM shows how those actions move the scene forward
- The players say how they continue to act