addEventListener on NodeList

The best I could come up with was this:

const $coins = document.querySelectorAll('.coins')
$coins.forEach($coin => $coin.addEventListener('dragstart', handleDragStart));

Note that this uses ES6 features, so please make sure to transpile it first!

There is no way to do it without looping through every element. You could, of course, write a function to do it for you.

function addEventListenerList(list, event, fn) {
    for (var i = 0, len = list.length; i < len; i++) {
        list[i].addEventListener(event, fn, false);
    }
}

var ar_coins = document.getElementsByClassName('coins');
addEventListenerList(ar_coins, 'dragstart', handleDragStart); 

or a more specialized version:

function addEventListenerByClass(className, event, fn) {
    var list = document.getElementsByClassName(className);
    for (var i = 0, len = list.length; i < len; i++) {
        list[i].addEventListener(event, fn, false);
    }
}

addEventListenerByClass('coins', 'dragstart', handleDragStart); 

And, though you didn't ask about jQuery, this is the kind of stuff that jQuery is particularly good at:

$('.coins').on('dragstart', handleDragStart);