Number 1: breadth of options. Games like rollercoaster tycoon are fun because you have an incredible range of options. There is no linear progression from start to finish with only a few choice points in between that have little impact. There are choices everywhere. The opposite is a game like mario, where there are almost no choices.
Number 2: reflexes. Games like pong and mario are fun because they require actions at the right timing. Turn based games do not have that.
Number 3: collection. You collect items or upgrades or in game currency that help you later. Although I have never played it myself, an example is World of Warcraft. You collect items, money and levels. There is something satisfying about this. Game designers often exploit it to make a game addictive.
Number 4: human adversaries. Playing against AI or against some in game metric (e.g. get X amount of people in your rollercoaster park) is not very fun. Playing against human opponents is much more fun because they are unpredictable and intelligent. It's not enough to just compete, there has to be interaction. If you put 2 games of tetris next to each other where the players compete for the highest score that's not good enough. First person shooters have this point right. The decisions of the players influence each other, rather than only competing via a score. Chess & go are the epitome of this.
The games that come closest to hitting all these points are real time strategy games. You have a large amount of options. Not as much as in a sandbox game like rollercoaster tycoon, but still far more than in the average game. You need reflexes to react to threats. You collect resources, upgrades and units. Last but not least, you have human opponents who also have a large amount of options that you need to react to. Not as strategic as chess, but far more so than your average game.
Sadly rts appears to be a dying genre...