ComboBox is pointing to TextBox which does not have all the same methods as ComboBox, namely loadAndOpenDropDown.
https://github.com/dojo/typings/blob/master/dijit/1.11/modules.d.ts#L274
I changed the above line to this to get it to work, however I don't know if this is 100% correct.
type ComboBox = dijit.form.ComboBox<any, any, any, any>;
Thanks!