In the 25-minute video, members of Wilayat Sinai (known previously as Ansar Beit Al-Maqdis) could be seen stopping trucks carrying cigarettes, emptying their cargo and setting it on fire.
One militant identified in the video as Abu Meqdad al-Masri described "smoking and drugs" as some of the evils faced by the group.
"Some people who smuggle large quantities of tobacco were prevented from doing so by Hisba men, who advised and then punished them, after which they prohibited the sale of tobacco or its promotion," he said.
Other scenes showed the militants smashing television sets and setting them on fire, as well as destroying gravestones, deemed religiously prohibited by extremists.
Islamic scholars define Hisba as the practice of commanding virtue and forbidding vice, but argue that it must be conducted by a select few entrusted with religious matters, Islamic law professor Ahmed Kareema told state-owned al-Ahram daily.
One of the militants showed in the video, identified as Abu Musaab al-Masry, said that enforcing Hisba was Wilayat Sinai's "top priority".
"We have referred sinners to the Sharia court, which will either sentence them to death or order them to repent," he said.
The video concluded with the beheading of two Sufi Sheikhs, after the militant described Sufism as a form of polytheism and heterodoxy.
Since the ousting of Islamist President Mohamed Morsi in a 2013 military coup, led by then defence minister and current President Abdel Fattah al-Sisi, North Sinai has been caught in the crossfire between the army and local armed militants.
The majority of the Islamist militant attacks, in which hundreds of Egyptian security personnel have been killed, were carried out by Wilayat Sinai, which has officially pledged allegiance to IS. A state of emergency has since been in place in some parts of North Sinai.
The group has been accused of carrying out recent targeted attacked against Coptic Christians in North Sinai after seven were killed by militants in February.
Earlier this month, hundreds of Copts fled the North Sinai city of al-Arish to escape the latest spate of targeting Christians.
The latest in a string of sectarian attacks came after the group released a video threatening further attacks on Egypt's Christian minority.
In the video, the group also claimed responsibility for last December's bomb explosion in a chapel beside Cairo's Coptic cathedral that left more than 25 dead and dozens injured.
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