[Solved]-Hide dataLabels at specific chart width in Highcharts-Highcharts

Do not attempt to re-init the chart with:

chart = new Highcharts.Chart(options);

Instead use the series update method.

function responsiveText(){

    Highcharts.charts[0].series[0].update({
        dataLabels: {
            enabled: !($('#container').width() < 578)
        }
    }, true);

}

Fiddle demo here.