TwilioQuest is available to download on Mac, Windows, and Linux machines, with a step-by-step guide provided for those who want to play on a Chromebook. To start playing TwilioQuest on a Chromebook, users need to enable the Linux (beta) option, which may result in reduced performance of the game. The installation process involves downloading the game, navigating to the settings area, and installing Linux, followed by installing the .deb installer using the terminal or dragging it to the "Linux files" folder. Once installed, users can play TwilioQuest on their Chromebook.