For anyone else seeing this a few years later, here's what I did to enable right-click paste for my TinyMCE editor:
tinymce.init({
selector: ".TinyMceTextEditor",
plugins: "contextmenu",
contextmenu: "paste | link image inserttable | cell row column deletetable"
});
If you enable the contextmenu plugin, then you can specify the contextmenu itself and include "paste". This way you can bypass the default right-click context menu and still get the paste option (plus a lot of other functionality). The other options I have in the contextmenu are the defaults.