According to the BBC's Tom Stafford, games like Tetris are successful because they take advantage of a deep-seated psychological drive to tidy up.

Tetris holds our attention by continually creating unfinished tasks. Each action in the game allows us to solve part of the puzzle, filling up a row or rows completely so that they disappear, but is also just as likely to create new, unfinished work. A chain of these partial-solutions and newly triggered unsolved tasks can easily stretch to hours, each moment full of the same kind of satisfaction as scratching an itch.

The other reason why Tetris works so well is that each unfinished task only appears at the same time as its potential solution -- those blocks continuously fall from the sky, each one a problem and a potential solution. Tetris is a simple visual world, and solutions can immediately be tried out using the five control keys (move left, move right, rotate left, rotate right and drop -- of course). Studies of Tetris players show that people prefer to rotate the blocks to see if they'll fit, rather than think about if they'll fit. Either method would work, of course, but Tetris creates a world where action is quicker than thought -- and this is part of the key to why it is so absorbing. Unlike so much of life, Tetris makes an immediate connection between our insight into how we might solve a problem and the means to begin acting on it.

The Zeigarnik Effect describes a phenomenon, but it doesn't really give any reason for why it happens. This is a common trick of psychologists, to pretend they solved a riddle of the human mind by giving it a name, when all they've done is invented an agreed upon name for the mystery rather than solved it. A plausible explanation for the existence of the Effect is that the mind is designed to reorganise around the pursuit of goals. If those goals are met, then the mind turns to something else.