pure javascript to check if something has hover (without setting on mouseover/out)

You can use querySelector for IE>=8:

const isHover = e => e.parentElement.querySelector(':hover') === e;    

const myDiv = document.getElementById('mydiv');
document.addEventListener('mousemove', function checkHover() {
  const hovered = isHover(myDiv);
  if (hovered !== checkHover.hovered) {
    console.log(hovered ? 'hovered' : 'not hovered');
    checkHover.hovered = hovered;
  }
});

.whyToCheckMe {position: absolute;left: 100px;top: 50px;}

<div id="mydiv">HoverMe
  <div class="whyToCheckMe">Do I need to be checked too?</div>
</div>

to fallback I think it is ok @Kolink answer.

Simply using element.matches(':hover') seems to work well for me, you can use a comprehensive polyfill for older browsers too: https://developer.mozilla.org/en-US/docs/Web/API/Element/matches

First you need to keep track of which elements are being hovered on. Here's one way of doing it:

(function() {
    var matchfunc = null, prefixes = ["","ms","moz","webkit","o"], i, m;
    for(i=0; i<prefixes.length; i++) {
        m = prefixes[i]+(prefixes[i] ? "Matches" : "matches");
        if( document.documentElement[m]) {matchfunc = m; break;}
        m += "Selector";
        if( document.documentElement[m]) {matchfunc = m; break;}
    }
    if( matchfunc) window.isHover = function(elem) {return elem[matchfunc](":hover");};
    else {
        window.onmouseover = function(e) {
            e = e || window.event;
            var t = e.srcElement || e.target;
            while(t) {
                t.hovering = true;
                t = t.parentNode;
            }
        };
        window.onmouseout = function(e) {
            e = e || window.event;
            var t = e.srcElement || e.target;
            while(t) {
                t.hovering = false;
                t = t.parentNode;
            }
        };
        window.isHover = function(elem) {return elem.hovering;};
   }
})();