Here is how Roosevelt began the last paragraph of that speech:
Finally, it would be a masterstroke if those great powers honestly bent on peace would form a League of Peace, not only to keep the peace among themselves, but to prevent, by force if necessary, its being broken by others. The supreme difficulty in connection with developing the peace work of The Hague arises from the lack of any executive power, of any police power to enforce the decrees of the court.
Even here, TR continues his zeal for kingly government and some power, any power, who can issue decrees to all of you little peasants out there. But this is much, much worse. Being as this speech is from 1910, this makes Roosevelt the first American President(he was a former president at the time) to call for an international body to lord over multiple nations. Note that last line, where he laments the fact that there's no executive power at the Hague. So, to you living in 2016, do you think Roosevelt would be proud of what his World Court has become? It's just a side question, a thought piece.
Woodrow Wilson would continue Roosevelt's work with an attempt to form a
League of Peace League of Nations, and finally, TR's cousin Franklin would succeed in implementing the dream, with the introduction of the League of Peace United Nations.