Can Original Xbox Games Play on Xbox 360?

No. Original Xbox games (2001–2005) do not work on Xbox 360.

Why Not?

• Different Architecture: Original Xbox = Intel Pentium III (x86) + NVIDIA NV2A. Xbox 360 = IBM PowerPC Tri-Core + ATI Xenos. Completely incompatible instruction sets and GPU APIs.
• No Software Emulation Layer: Unlike Xbox One/Series X|S (which emulate Xbox 360 and original Xbox), the 360 never received an original Xbox emulator.
• Disc Format: Both use DVD, but filesystem/layout and encryption differ.

Forward Compatibility

Xbox 360 games DO play on Xbox One and Xbox Series X|S via Microsoft's backward compatibility program (hundreds of titles, often enhanced).

To play original Xbox games today: use an original Xbox, a softmodded Xbox (XBMC/Emulators), or PC emulation (Xemu, CXBX-Reloaded).