The good thing about Highcharts is that it works perfectly well on both desktop browsers and web mobile environments without requiring any change of code. The only part that needs some consideration is events handling, because mobile devices are all touch-screen based and that means the mouse cursor is invisible.
In Highcharts, all the mouse hover events can still be triggered in touch devices, even though the mouse cursor is not shown. For instance, suppose we define a series with the mouseOut, mouseOver, and click events handling. If we touch the series, both the mouseOver and click events are triggered. However, if we touch another series causing the previous selected series to be unselected, a mouseOut event for the first series is fired. Needless to say, the sequence of events would be different with a real pointing device. In general, we should refrain from using any mouse hover events in touch-screen based devices.