Make GlobalEventHandlers not inherit from EventTarget

tools/dom/templates/html/impl/impl_GlobalEventHandlers.darttemplate

Index: tools/dom/templates/html/impl/impl_GlobalEventHandlers.darttemplate
diff --git a/tools/dom/templates/html/impl/impl_GlobalEventHandlers.darttemplate b/tools/dom/templates/html/impl/impl_GlobalEventHandlers.darttemplate
index d1b4f836fcd7cd859ea25a75c4519609cc18c5ce..af140f7778b826f108e7f1f13a2fa0d0f8bf641e 100644
--- a/tools/dom/templates/html/impl/impl_GlobalEventHandlers.darttemplate
+++ b/tools/dom/templates/html/impl/impl_GlobalEventHandlers.darttemplate
@@ -4,6 +4,15 @@
 
 part of $LIBRARYNAME;
 
+// We implement EventTarget and have stubs for its methods because it's tricky to
+// convince the scripts to make our instance methods abstract, and the bodies that
+// get generated require `this` to be an EventTarget.
 @DocsEditable()
-$(ANNOTATIONS)$(NATIVESPEC)$(CLASS_MODIFIERS)class $CLASSNAME extends EventTarget {
+$(ANNOTATIONS)$(NATIVESPEC)$(CLASS_MODIFIERS)class $CLASSNAME implements EventTarget {
+
+  void addEventListener(String type, dynamic listener(Event event), [bool useCapture]);
+  bool dispatchEvent(Event event);
+  void removeEventListener(String type, dynamic listener(Event event), [bool useCapture]);
+  Events get on;
+
 $!MEMBERS}