Java Incompatibility: RuneScape (originally Java-based, now C++ NXT client) requires a full desktop OS (Windows/macOS/Linux) or Android/iOS. The Wii's Opera-based browser and custom OS cannot run the client.
No Official Port: Jagex never developed a Wii version.
Control Scheme: Point-and-click + keyboard-heavy UI doesn't translate well to Wii Remote.