Initially when there's no opacity set, the value will be an empty string, which will cause your arithmetic to fail. That is, "" < 0.1 == true and your code goes into the clearInterval branch.
You can default it to 1 and it will work.
function fadeOutEffect() {
    var fadeTarget = document.getElementById("target");
    var fadeEffect = setInterval(function () {
        if (!fadeTarget.style.opacity) {
            fadeTarget.style.opacity = 1;
        }
        if (fadeTarget.style.opacity > 0) {
            fadeTarget.style.opacity -= 0.1;
        } else {
            clearInterval(fadeEffect);
        }
    }, 200);
}
document.getElementById("target").addEventListener('click', fadeOutEffect);
#target {
    height: 100px;
    background-color: red;
}
<div id="target">Click to fade</div>
 
 
An empty string seems like it's treated as a 0 by JavaScript when doing arithmetic and comparisons (even though in CSS it treats that empty string as full opacity)
> '' < 0.1
> true
> '' > 0.1
> false
> '' - 0.1
> -0.1
Simpler Approach
We can now use CSS transitions to make the fade out happen with a lot less code
const target = document.getElementById("target");
target.addEventListener('click', () => target.style.opacity = '0');
// If you want to remove it from the page after the fadeout
target.addEventListener('transitionend', () => target.remove());
#target {
    height: 100px;
    background-color: red;
    transition: opacity 1s;
}
<p>Some text before<p>
<div id="target">Click to fade</div>
<p>Some text after</p>