Is it correct to describe the fight between Imam Ali (A.S) and Muawiyah as being a jihad?

After the battle of Siffin, Muawiyah carried out a series of massacres within cities of Imam Ali’s domain. To this end he sent his general Sufyan ibn Awf al-Ghamidi with a force of 6,000 to attack three towns, Hit, al-Anbar and Madain. When he reached Madain and found it deserted he marched on al-Anbar. The atrocities committed were so enormous that Imam Ali (A.S) was obliged to exhort people to jihad to defend themselves.

Surely jihad is one of the doors of paradise, which Allah has opened for his true supporters.
It is the dress of piety and the protective armour of Allah and is His trustworthy shield.
Whoever abandons it is adorned by Allah in the dress of disgrace.

I called you to fight these people night and day, secretly and openly but you put it off to others and forsook doing that until destruction befell you and your cities were occupied. The horsemen of Banu Ghamid have reached al-Anbar and killed Hasan ibn Hasan al-Bakri and removed your horsemen from the garrison. I have learned that every one of them entered into Muslim women as well as those Christians and others under the protection of Islam and removed the ornaments from their legs, arms, necks and ears, which none were able to resist. They then returned home laden with this wealth without wounds or loss of life. If any Muslim dies of grief after all this he is not to be blamed for, in my opinion, there is justification for that to have occured. Nahjul Balagha, Sermon 27

In the above sermon, Imam Ali (A.S) describes fighting against Muawiyah and his troops who committed genocide as a jihad. It is evident that the Imam was not only supporting
Muslim women, but also seeking the safety of non-Muslims under the protection of the Islamic state – dhimmis.