I found the documentation for this (http://api.highcharts.com/highcharts#tooltip.pointFormat). The HTML they're using is located under pointFormat, not formatter:
<span style="color:{point.color}">\u25CF</span> {series.name}: <b>{point.y}</b><br/>
Here's the updated code to use to get the colored circles in the tooltip:
tooltip: {
formatter: function() {
var s = '<b>'+ this.x +'</b>';
$.each(this.points, function(i, point) {
s += '<br/><span style="color:' + point.color + '">\u25CF</span> ' + point.series.name + ': ' + point.y;
});
return s;
},
shared: true
},