"this"- in your code refers to the element for which you have bound the click event.
The Backend API is available for extension developers as this.backend API, in order to have the backend API to work you should use "this" which is referring/points to the extension itself
Example
var self = this; // referring to the extension itself & should be declared within the paint method
$element.on('click',function(){ var value =[1,2]; self.backendApi.selectValues(0, value,true);