From the linked webpage:
This prohibition on punishing anyone by burning with fire is general in application, but the majority of scholars made an exception in the case of burning with fire by way of retaliatory punishment (qisaas) and making the punishment fit the crime. If someone burns another person then it is permissible, according to this view, to punish him by burning him, by way of retaliatory punishment.
They quoted as evidence for that the verses in which Allah, may He be exalted, says (interpretation of the meaning):
“Then whoever transgresses the prohibition against you, you transgress likewise against him. And fear Allah, and know that Allah is with Al-Muttaqoon (the pious)”
“And if you punish (your enemy, O you believers in the Oneness of Allah), then punish them with the like of that with which you were afflicted. But if you endure patiently, verily, it is better for As-Sabirin (the patient ones, etc.)”
The basic principle says that acting upon two sound texts that have not been abrogated is better than overlooking one of them.
For more information, please see fatwa no. 147416
Therefore the majority of fuqaha’ think that it is permissible to burn with fire by way of retaliatory punishment.
Ibn Mulaqqin (may Allah have mercy on him) said:
One group of scholars said: Whoever burns is to be burnt. This is also the view of Maalik, the scholars of Madinah, ash-Shaafa‘i and his companions, Ahmad and Ishaaq.
I apologise for the delay in replying to your post. I've drafted a response, but have yet to finalise it (time constraints). No disrespect is intended. In šāʾ Allāh, I'll come back soon.
May Allāh (Subḥānahu ūta'āla) reward you for your patience.