No, the address in not correct. As you say, Complejo de la Moncloa is correct (I also checked the official page)
But there is not “Republic of Spain” since 1939. That country doesn’t exist now. Spain, now, is a kingdom and her king is Juan Carlos I. That should say “Kingdom of Spain”. It’s funny because it’s not the first time: Jeb Bush also made the same mistake in a conference in Spain a couple of years ago, and in a tennis championship in Australia, they put the republican national music (Himno de Riego) instead the used now (Marcha Real). Imagine the face of Spannish tennists :lol:
And Rodriguez Zapatero is not the Prime Minister. He is the President of the Government (even if he makes basically the same than UK Primer Minister)
Is also funny that such errors sometimes happen in Spain. Not the republican"" error, but sending letters to a non-existant minister or to a place where the official building was there 5 years ago but now is in another place :-D