At first glance playing and gaming are two words that we use to convey the same concept. They are colloquially interchangeable in some contexts but not in others. You can say that you play a game, you can play the game of hopscotch or football. Or you can play BATTLEFIELD ( and you should! )!
The key to an engaging gaming experience for me is the art of problem creation and motivation. As a developer you need to con the gamer into caring about what happens next, and isolate him from 'next' by an obstacle. If somebody has bought your game he/she will play through it (or at least most of it ). I bought "Alone In The Dark The New Nightmare", haven't finished it, never buying another Infogrames title ever again ( ever )! But at that point the idiots in marketing have done a good job, not you ( the developer )! You have done a good job when somebody sits down to play your game and stops playing when the alarm clock goes off to inform him it's time to get up ( as in it's morning ( as in he played all night )). When talking about motivation there are several separate components, but the most important one are the obstacles a.k.a gameplay. Games are fun because they present a problem solving challenge and good games are highly stimulating to the brain. Good games should'n be easy, but they should'n be so hard that they stress the gamer. I prefer a serious challenge but it isn't a must for a game to grab your attention, even easy tasks can keep the gamer engaged and entertained! Most games use alternation between moments of pressure and moments of calm. Reaching a perfect challenge level is impossible since it is subjective, that is why games ask for the gamer's preferred difficulty level. Control scheme and mechanics shouldn't contribute to difficulty, clunky controls don't raise difficulty, they are just frustrating. Exactly why is Mario always running to the right, to save the princes or to see the end of the level? Mario is actually running right to see what is to the right of the screen! In a sense Mario is an obstacle junkie who passes obstacles to reach more obstacles to pass. In games it really is the thrill of the chase and not the reward, since there isn't any reward, except the false feeling of accomplishment in the end!
When thinking about what a good game is, I think of the games that have made me stay up all night. Than I try and dissect them into separate components and find which of them kept me playing, but it is never a single thing. A good game maybe doesn't have the best story or gameplay or technology. But it does have a nice fit between it's parts, and it has that slightly original and slightly familiar appeal that keeps me engaged for hours.