~root
is a reference to the data object or array you passed in initially - the top-level data. It is not the immediate parent data. In your case ~root will be the {}
you passed in with the link.myTemplate()
call.
Update added later: (Response to question in comment below about ~root)
From JsViews point of view, when any block tag content is rendered, it is also a 'view' - where a template is rendered against data. The views make up a hierarchy, and the top-level one is the one for which the data is exposed as ~root. So if you want to provide special short cut aliases for data at intermediate levels, you can do so, but that is for you to do. Declaratively that is done as in this example. In your case you are calling the intermediate level template render programmatically, so you can do the equivalent by providing a reference as a context variable:
return $.templates.test1.render(
this.tagCtx.props,
{mydata: this.tagCtx.props},
this.tagCtx.view);
Now you can write
<script id="test1Template" type="text/x-jsrender">
<div>{^{>title}}{{:content}}</div>
{{test2}}
<h1>{^{>~mydata.title}}</h1>
{{/test2}}
</script>