I identified several overarching concepts that hook players into wanting to continue playing a game. This is meant in a positive way; they want to keep playing because these things cause the game experience to be intriguing / fun.
My goal in game design is to maximize the opportunities for these hooks and to have them synergize to the greatest extent achievable. It is basically my version of the MDA framework.
ANTICIPATION PLOT The desire to know what's going to happen next. EXPLORATION The desire to know what's around the corner. EXCEPTION The anticipation of something rare occurring. The player must be provided with the knowledge of something exceptionally rare and/or undiscovered existing. ... ORDER COLLECTING The desire to bring order to a collection by completing it. The collectibles must be unique as they need to belong to a finite set that can be realistically completed. The collection and its current progress should be visualized either in an GUI or - even better - directly within the game world. Bonus points if the collectibles contribute meaningfully to game mechanics. PUZZLES The desire to bring order to puzzles by solving them. As part of a greater game world, solving puzzles should be linked to progression or some kind of reward that has meaning in the greater context. FIXING AND UPGRADING Reaching new heights by improving something is exhilarating. ... PRESSURE TIME PRESSURE The pressure of time can cause adrenaline in the rush of the moment. An example of its implementation is a fast paced action combat system. The player must be provided with all the necessary information to make a beneficial decision in a timely manner - otherwise being punished will feel unfair and frustrating. CONSEQUENCE PRESSURE A multiple choice with different outcomes. The player must be provided with at least a rough understanding of what consequences the available choices have. COMPETITION Being driving by the challenge of competition. ... ATTACHMENT CHARM Being attached to game sceneries or entities - particularly to the playable character(s) - can by itself make the player continue to come back to the game. This can be aided by the character being a visual expression of a power fantasy, or otherwise attractive. Of course a relatable backstory helps, too. SELF-EXPRESSION Having put in effort to improve and customize the playable character builds attachment. Ideally, customizable elements (that player had to put effort in to unlock) are displayed on the playable character. NOSTALGIA Many people had their childhood defined by certain games. Invoking these memories can easily hook people, but it's questionable if it makes sense to attempt to target an audience that way. It's probably best to not look for things other people may feel nostalgic about, but to put in things I myself (e.g. dev team) feel fondly for. ...
This is of course not inclusive, so I may add to it over time. Still, I believe that pretty much all of these things can be categorized in a very small number of fundamental human drives. The powerful thing about that realization is that once the overarching concept has been identified, it's relatively easy to find additional kinds of hooks. For example, once I realized that what makes stories captivating is really an expression of anticipation, I could think about other tools that can be used to build anticipation. Similarly, wanting to complete a collection is really just the drive to bring order into things, and solving puzzles tabs into that same desire.