In a Nutshell: For any country to claim to be Islamic, its driving ideology must be solely Islam, namely its laws must have evidence from the Qur'an, Sunnah, Qiyas and Ijma as-Sahabah. What renders any ruling, judgment or idea Islamic is not its use of Islamic terminology or it coming from an Islamic scholar, but its reliance on and derivation from an authentic daleel through a correct process of Ijtihad.
The constitution of the Islamic Republic of Iran has many articles which comply with Islam but there others which directly conflict with it - rooted in secular ideologies like nationalism or copied Western forms of government.