We are talking about "Islamic peace" As prescribed by the creator. It inherently means that Muslims(believers) by default must be the holders of the Law as prescribed by the creator. That being said the chart you shared has some inconsistencies mainly being Dhimma is mainly done with a tribe or people that run their affairs and Zakat is a more individual thing.
Here is an excerpt;
"The treaty of protection made by Khalid ibn Al-Walid with the Christians of Al-Hira in Iraq states:
Any aged non-Muslim who is unable to earn his livelihood, or is struck by disaster, or who becomes destitute and is helped by the charity of his fellow men will be exempted from the capitation tax and will be supplied with sustenance by the bait al-mal (the government treasury). (Abu Yusuf, Al-Kharaj, p. 144)
The obligation of paying this tax is also cancelled when non-Muslims participate with Muslims in defending the Islamic state against its enemies. Such conditions were clearly stated in contracts and other documents signed by Muslims and non-Muslims during the reign of Umar ibn Al Khattab. (See Zeidan, 'Abdul Karim, Ahkam-Dhimmiyin Wa Al-Musti'minin Fi Dar Al-Islam, p. 155 ff, and Al-Baladhuri, Futuh Al-Buldan, p. 217, where it is stated that the emissary of Abu 'Ubaida made a compromise with a party of the Christian Jarajima: if they would support the Muslims and keep an eye on their enemies, they would not have to pay the Jizyah)
Should the Islamic state become unable to abide by the contract, it may not collect the Jizyah. This rule was followed by Abu 'Ubaidah when he learned of the situation in several Syrian cities. Syria had fallen into the hands of the Muslims, but as the Romans were gathering troops to regain it, he decided not to undertake the protection of the non-Muslims. The Jizyah was, therefore, returned with the announcement:
We have returned your money to you because we have been informed of the gathering of the enemy troops. You people, according to the conditions stipulated in the contract, have obliged us to protect you. Since we are now unable to fulfill these conditions, we are returning your money to you. We will abide by the conditions as agreed upon if we overcome the enemy. (Related by Abu Yusuf in Al-Kharaj)
Thus, a huge amount was taken from the state treasury and returned to the Christians, making them very happy. They prayed for and blessed the Muslim commanders. They exclaimed,
"May Allah help you to overcome your enemies and return you to us safely. If the enemy were in your place, they would never have returned anything to us, but rather they would have taken all our remaining property. (Imam Tabari, Tarikh At-Tabari, Volume 1, p. 2050)
The Jizyah was also imposed on Muslim men who could afford to buy their way out of military service. If a Christian group elected to serve in the state's military forces, it was exempted from the Jizyah. Historical examples of this abound: the Jarajima, a Christian tribe living near Antioch (now in Turkey), by undertaking to support the Muslims and to fight on the battle front, did not have to pay the Jizyah and were entitled to a share of the captured booty. (Al-Baladhuri, p. 159) When the Islamic conquests reached northern Persia in 22 A.H., a similar covenant was established with a tribe living on the boundaries of those territories. They were consequently exempted from Jizyah in view of their military services. (Ibid.)"
