Backer Ruth fills out Riku's theme beautifully with a driving beat and a variety of additional instruments. Its steady and persistent style is perfectly suited for Riku's journey towards self-redemption.
Riku's theme is utilized particularly effectively during 358/2 Days, in which Riku works behind the scenes, trying to orchestrate Sora's awakening in collaboration with DiZ and Naminé. Most prominently, it appears as Riku defeats Xion outside of Beast's Castle midway through the game.
Riku's story arc runs on his tenacity. He's willing to do whatever it takes to make things right again. Along the way, he's forced to make several sacrifices to save Sora. Xion's very existence becomes a major moral conflict, as her absorption of Sora's memories makes it impossible for him to awaken. In this early scene, Riku, dressed in an Organization cloak, remarks that Xion's keyblade is a sham. When Xion asks him who he is, he answers that he "is the biggest nobody of them all." Cue spine-chilling Xion scream of frustration.
This scene, and the accompanying track, are so important to Riku's character because it isn't just Roxas and Xion's existences that he has to contend with. Riku essentially gives up his own life and future to fix what's been broken. Whatever it takes "to make sure [his] best friend sleeps in peace."