Will Kingdom Hearts 1 Ever Release on Xbox 360? No.

No. Kingdom Hearts (the first game) has never been released on Xbox 360, and it never will.

Reasons

• Platform exclusivity – Original (2002) was PS2 exclusive. HD remasters (1.5 + 2.5) released on PS3, PS4, Xbox One, Switch, PC—skipping 360 entirely.
• Engine & licensing – Disney/Square Enix contracts historically favored PlayStation; porting to 360's architecture (PowerPC, unique GPU) was deemed not worthwhile late in its lifecycle.
• Timeline – By the time multiplatform releases began (2013+), Xbox 360 was succeeded by Xbox One.

How to Play Kingdom Hearts 1 Today

• Kingdom Hearts HD 1.5 ReMIX – PS3, PS4, Xbox One, Switch, PC (Epic/Steam).
• Original PS2 disc – On backward-compatible PS3 or via PS2 Classics on PS4/PS5 (streaming).

If you only have an Xbox 360, you cannot play Kingdom Hearts 1 officially.