Edit in JSFiddle

<body>
<h1>
基本のマウスストーカー
</h1>
<div id="mouse-stalker"></div>
</body>
#mouse-stalker {
    pointer-events: none;
    position: fixed;
    top: -10px;
    left: -10px;
    width: 20px;
    height: 20px;
    background: rgba(0,165,160,0.5);
    border-radius: 50%;
    transform: translate(0,0);
    transition: transform 0.2s;
    transition-timing-function: ease-out;
    z-index: 999;
}

/* 以下、関係のない記述です。 */
body {
    margin: 20px;
    text-align: center;

  h1 {
    font-size: 20px;
    font-weight: bold;
    margin-bottom: 20px;
  }
}
const stalker = document.getElementById('mouse-stalker'); 
document.addEventListener('mousemove', function (e) {
    stalker.style.transform = 'translate(' + e.clientX + 'px, ' + e.clientY + 'px)';
});