Organize JavaScript for video player controls
This looks just fine to me.

Some very minor nitpicks:


Remove //console.log(chapterTime);
Consider removing the blank line after var statements, it does not add much
chapterTime could use a comment as to what those numbers express (I assume seconds)
I would probably write this

buttons.delegate('click', function () {
    var button_name =  this.ancestor().get('id'),
        chapter = button_name.slice(1);

        playChapter(chapterTime[chapter-1], this);
}, 'a');   


as

buttons.delegate('click', function () {
        var chapter = this.ancestor().get('id').slice(1) - 1;
        playChapter(chapterTime[chapter], this);
}, 'a');   

The color strings #999 and #666 have a meaning, I assume enabled/disabled, you could use properly named constants for these, declared on top
Only seldom use double newlines, they are vertical overkill


Still, all in all I like your code.