You need to add this at the top:
declare var require: any;
In general I suggest you install highcharts module instead of using npm install angular2-highcharts:
$ npm install highcharts --save 
Then you can declare Highcharts like this:
declare var require: any;
let hcharts = require('highcharts');
require('highcharts/modules/exporting')(hcharts);
Here's a full example:
import { ElementRef, Component} from '@angular/core';
import { NavController } from 'ionic/angular';
declare var require: any;
let hcharts = require('highcharts');
require('highcharts/modules/exporting')(hcharts);
@Component({
    selector: 'page-about',
    template: `<div #myChart></div>`,
})
export class AboutPage {
    @ViewChild('myChart') canvas: ElementRef;
    constructor(public navCtrl: NavController) {}
    ionViewDidLoad() {
        let chart = hcharts.chart(this.canvas.nativeElement, {
            chart: {
                zoomType: 'x',
                events: {
                    load: function() {
                        let self = this;
                        setTimeout(function(){
                            self.reflow();
                        }, 100);
                    }
                }
            },
            series: [{
                data: [1, 3, 2, 4]
            }],
        });
    }
}