In the page you linked the template is stored in an external html file in which case you get syntax checking for html but not the embedded expressions.
I only do backend node.js so I don't know much about the frontend stuff, but when I look at
https://blog.jetbrains.com/webstorm/2016/04/angular-2-workfl...
it seems to me they in fact do support the embedded expressions?
https://www.jetbrains.com/webstorm/whatsnew/#v2016-2-angular...
I do agree that I really really was a fan of the backticks for ES6 / react for templating. Avoiding the whole " vs ' escaping nightmare is something i've always looked forward to.
That seems like a very simple fix for them though, potentially.
edit: tone