Are those calling for rule of Islam called khawarij?

They most certainly are not. إِنِ الْحُكْمُ إِلَّا لِلَّهِ ۚ أَمَرَ أَلَّا تَعْبُدُوا إِلَّا إِيَّاهُ ۚ ذَٰلِكَ الدِّينُ الْقَيِّمُ وَلَٰكِنَّ أَكْثَرَ النَّاسِ لَا يَعْلَمُونَ “The Hukm (Legislating, Commands, Judgment) is for none but Allah. He has commanded that you worship none but Him, that is the (true) straight religion, but most men know not.” (Quran 12:40) Imam al-Baghawi (died 509AH) commented on Quran Chapter 12:40 in Tafsir ul-Baghawi, Vol 2, Pg. 427, saying, “Indeed the (Right of) ruling, commanding and prohibiting is for none but Allah” In another verse, Allah says: مَا لَهُم مِّن دُونِهِ مِن وَلِيٍّ وَلَا يُشْرِكُ فِي حُكْمِهِ أَحَدًا “…and He makes none to share in His Judgment and His Rule.” [Quran, Surah, 18:26] Imam at-Tabari (died 311AH) explained this verse in Tafsir ut-Tabari, Vol 8, Page 212, saying, “Allāh will never let His creation be a partner in His ruling and judgment. He is indeed the only One Who rules (legislates) and judges, and He manages them (the creations) in whatever way He wills” The following verses show the Shirk of worshiping others besides Allāh in His Judgment and Legislation and there is absolutely no difference between the one who prostrate to idols and the one who commit Shirk with Allāh in His Judgment and Legislation. Both are Mushriks (polytheists). أَمْ لَهُمْ شُرَكَاءُ شَرَعُوا لَهُم مِّنَ الدِّينِ مَا لَمْ يَأْذَن بِهِ اللَّهُ “Or have they partners with Allah (false gods), who have permitted for them a Deen (law, way of life or religion) which Allah has not allowed.” (Quran 42:21) أَلَمْ تَرَ إِلَى الَّذِينَ يَزْعُمُونَ أَنَّهُمْ آمَنُوا بِمَا أُنزِلَ إِلَيْكَ وَمَا أُنزِلَ مِن قَبْلِكَ يُرِيدُونَ أَن يَتَحَاكَمُوا إِلَى الطَّاغُوتِ وَقَدْ أُمِرُوا أَن يَكْفُرُوا بِهِ وَيُرِيدُ الشَّيْطَانُ أَن يُضِلَّهُمْ ضَلَالًا بَعِيدًا “Have you seen those (hypocrites) who claim that they believe in that which has been sent down to you, and that which was sent down before you, and they wish to go for judgment (in their disputes) to the taghut (false judges) while they have been ordered to reject them. But Shaytan (Satan) wishes to lead them far astray.” (Quran 4:60) وَلَا تَأْكُلُوا مِمَّا لَمْ يُذْكَرِ اسْمُ اللَّهِ عَلَيْهِ وَإِنَّهُ لَفِسْقٌ ۗ وَإِنَّ الشَّيَاطِينَ لَيُوحُونَ إِلَىٰ أَوْلِيَائِهِمْ لِيُجَادِلُوكُمْ ۖ وَإِنْ أَطَعْتُمُوهُمْ إِنَّكُمْ لَمُشْرِكُونَ اتَّخَذُوا أَحْبَارَهُمْ وَرُهْبَانَهُمْ أَرْبَابًا مِّن دُونِ اللَّهِ وَالْمَسِيحَ ابْنَ مَرْيَمَ وَمَا أُمِرُوا إِلّا لِيَعْبُدُوا إِلَٰهًا وَاحِدًا ۖ لَّا إِلَٰهَ إِلَّا هُوَ ۚ سُبْحَانَهُ عَمَّا يُشْرِكُونَ “They (Jews and Christians) took their rabbis and their monks to be their lords besides Allah” (Quran 9:31) Once while Allah’s Messenger (saw) was reciting this verse, Adi bin Hatim (ra) said, ‘O Allāh’s Messenger! They do not worship them (i.e. the rabbis and monks)’. Allah’s Messenger (peace and blessings of Allah be upon him) said: ‘Yes they did. They (rabbis and monks) prohibited the allowed for them (Christians and Jews) and allowed the prohibited, and they obeyed them. This is how they worshiped them’. (Ahmad, at-Tirmidhi and Ibn Jarir) فلا وربك لا يؤمنون حتى يحكموك فيما شجر بينهم ثم لا يجدوا في أنفسهم حرجا مما قضيت ويسلموا تسليما But no, by your Lord, they will not [truly] believe until they make you, [O Muhammad], judge concerning that over which they dispute among themselves and then find within themselves no discomfort from what you have judged and submit in submission. (Quran 4:65) أفحكم الجاهلية يبغون ۚ ومن أحسن من الله حكما لقوم يوقنون Then is it the judgement of [the time of] ignorance they desire? But who is better than Allah in judgement for a people who are certain [in faith]. Those who rule by other than what Allah has revealed are disbelievers, wrongdoers and oppressors (Quran 5:50)