I think there is no one way of answering this without painting with an extremely broad stroke. For myself, I look for a game that keeps me engaged and focused. A game that has me thinking of different strategies and tactics to win. This competitive desire might not be shared though by others. Some may look for the storyline, or social aspects a game can have. Overall though, I believe games in the simplest terms are meant to be a fun challenge for people to entertain themselves with.
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