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It's not a proper adjective, and therefore should not be capitalized. The name "adventure" is generic. It's not like saying "This game is in the Zork genre," referring to a particular early game.
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#4: Attribution notice removed
Source: https://writers.stackexchange.com/a/2939 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#3: Attribution notice added
Source: https://writers.stackexchange.com/a/2939 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/