Is Pokémon Mystery Dungeon on Xbox 360?

No. The Pokémon Mystery Dungeon series is developed by Spike Chunsoft and published by Nintendo/The Pokémon Company. It is exclusive to Nintendo platforms:

• Red/Blue Rescue Team — GBA / DS (2005/2006)
• Explorers of Time/Darkness/Sky — DS (2007–2009)
• Gates to Infinity — 3DS (2012/2013)
• Super Mystery Dungeon — 3DS (2015/2016)
• Rescue Team DX — Switch (2020)

No mainline or spin-off Pokémon game has ever released on Xbox, PlayStation, or PC (except Pokémon GO / UNITE / TCG Live / Café ReMix on mobile).