chore(build): enable type-checking for TypeScript ES6 emit.

This requires delicate handling of type definitions which collide, because
we use TypeScript-provided lib.d.ts for --target=es5 and lib.es6.d.ts for
--target=es6.
We need to include our polyfill typings only in the --target=es5 case,
and the usages have to be consistent with lib.es6.d.ts.
Also starting with this change we now typecheck additional modules,
so this fixes a bunch of wrong typings which were never checked before.

Fixes #3178

modules/benchmarks/src/tree/tree_benchmark.ts

@@ -207,7 +207,7 @@ class BaseLineIf {
         this.component = null;
       }
       if (this.condition) {
-        var element = DOM.firstChild(DOM.clone(BASELINE_IF_TEMPLATE).content);
+        var element = DOM.firstChild((<any>DOM.clone(BASELINE_IF_TEMPLATE)).content);
         this.anchor.parentNode.insertBefore(element, DOM.nextSibling(this.anchor));
         this.component = new BaseLineTreeComponent(DOM.firstChild(element));
       }