This article from June has him passing Kinugasa's second place record of 678 consecutive games playing every inning of every game, not his 2,215 consecutive game feat (to which Kanemoto has a long way to go at "just" 846 games).
After this, Kanemoto went on to overtake former Hanshin Tiger Nobukazu Miyake who played every inning of 700 games before being hit in the left eye on September 6, 1962, stopping Miyake's streak.
Then end of the 2004 season saw Kanemoto's record standing at 750 (and counting) consecutive games without sitting out a single batter.
Cal Ripken does hold the world record in this category as well, playing every inning of 902 consecutive games. With good health, Kanemoto will be challenging that record in 2006.
I hope this clears up the confusion between the two records.
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When questioned by the press about his feat, Kanemoto said words to the effect of, "You can't compare me to Kinugasa; that's an affront to him. He appeared in 2,000 straight games (all innings or otherwise)."
Disclaimer: I haven't verified any of the above figures. I just copied them straight out of SanSpo.