String.prototype.includes is, as you write, not supported in Internet Explorer (or Opera).
Instead you can use String.prototype.indexOf. #indexOf returns the index of the first character of the substring if it is in the string, otherwise it returns -1. (Much like the Array equivalent)
var myString = 'this is my string';
myString.indexOf('string');
// -> 11
myString.indexOf('hello');
// -> -1
MDN has a polyfill for includes using indexOf: https://developer.mozilla.org/en/docs/Web/JavaScript/Reference/Global_Objects/String/includes#Polyfill
EDIT: Opera supports includes as of version 28.
EDIT 2: Current versions of Edge supports the method. (as of 2019)