If I understand your question correctly you would like to get the innerHTML of your created tag. That is as easy as "this.root.innerHTML".
<riot-tag>
asdfghjkl
<script>
this.on('updated', function(){
console.log(this.getInnerHTML());
});
getInnerHTML(){
return this.root.innerHTML;
}
</script>
</riot-tag>
If you need the innerHTML of any sub-element of your created tag set a name or id property on the element and reference it directly. Or if you are calling your function from an event, like click, have the element reference from e.target.
<riot-tag>
<h1 onclick={getInnerHTML} name="myTagHeader">asdfghjkl</h1>
<script>
getInnerHTML(e){
console.log(e.target.innerHTML);
console.log(this.myTagHeader.innerHTML);
}
</script>
</riot-tag>
Hope that it will help