It actually took quite a while for the games to be represented in fiction to a significant degree. Over time, the games saw themselves adapted to suit the needs of the viewing audience both in what they were and what they meant. This ranges from an initial misunderstanding, to shifts in the style of violence, to its very meaning.
The earliest ones fit a mold which I mentioned in the first part: the idea that the games themselves were caused by decadence rather than, as the Roman’s saw it, a treatment for it.
Science fiction stories were the ones to really run with this idea and find ways to exaggerate it in interesting ways.
Edgar Rice Burroughs, creator of Tarzan, incorporated the games into his Barsoom series, which the film John Carter is based on. Here, the decadence is caused by the alien beings of Barsoom (Mars) being unable to die in any way other than violence, and the entire world slowly dying. Immortality can get very boring, and they live in a brutal world.
Combine the two and bam! Instant excuse for death games.
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