No. Wii games cannot be played on Xbox 360.
| Aspect | Wii | Xbox 360 |
|---|---|---|
| CPU | IBM PowerPC "Broadway" (729 MHz) | IBM PowerPC "Xenon" Tri-Core (3.2 GHz) |
| GPU | ATI "Hollywood" (243 MHz) | ATI "Xenos" (500 MHz, Unified Shaders) |
| RAM | 88 MB (24+64) | 512 MB GDDR3 (Unified) |
| Disc | 8 cm DVD (1.4 GB / 4.7 GB DL) | 12 cm DVD-DL (8.5 GB) |
| OS | IOS (microkernel, per-game) | Xbox 360 Dashboard (Hypervisor) |
| Input | Wii Remote (IR, Accel), Nunchuk, Classic, GCN | Xbox 360 Controller (RF), Kinect |
Xbox 360 never received a Wii emulator (too weak for Wii emulation; Wii emulates GCN natively via hardware). PC (Dolphin) is the only viable cross-platform path.
Some games released on both (e.g., Call of Duty: World at War, Guitar Hero III, LEGO Star Wars) are separate builds. You must buy the Xbox 360 version.
Keep your Wii / Wii U / Switch for Wii library.