As of 2024, no official Hunger Games video game has been announced for Xbox (or any platform) since the mobile tie-ins (The Hunger Games: Girl on Fire 2012, Panem Run 2013) and the canceled The Hunger Games: District 12 (Facebook, 2011).
No credible leaks, job postings, or trademark filings suggest active development. The IP has been quiet in gaming since 2013. If announced, expect a 3–5 year dev cycle.
For now, the closest experiences are The Long Dark (survival), This War of Mine (civilian war), Disco Elysium (political RPG), or Fortnite (battle royale with Hunger Games skins/events).