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The init program is just the first process (PID 1) that the kernel starts. It starts other stuff and cleans up zombie processes.
For a single game: yes, you can absolutely just make your game PID 1. No need for systemd or anything else. When the game exits, the kernel panics and reboots.
ISO vs container: ISO boots on bare metal with your own kernel. Container needs a host kernel and runtime. If you're making a dedicated game appliance, the ISO approach works fine - simpler actually,
since you skip all the container orchestration machinery.