Can a ruler order the legal punishment on someone without himself being present?

Narrated Abu Huraira and Zaid bin Khalid Al-Juhani:

A man came to the Prophet and said, "I beseech you to judge us according to Allah's Laws." Then his opponent who was wiser than he, got up and said, "He has spoken the truth. So judge us according to Allah's Laws and please allow me (to speak), O Allah's Apostle." The Prophet ﷺ said, "Speak." He said, "My son was a laborer for the family of this man and he committed illegal sexual intercourse with his wife, and I gave one-hundred sheep and a slave as a ransom (for my son), but I asked the religious learned people (regarding this case), and they informed me that my son should be flogged one-hundred stripes, and be exiled for one year, and the wife of this man should be stoned (to death)."The Prophet ﷺ said, "By Him in Whose Hand my soul is, I will Judge you (in this case) according to Allah's Laws. The one-hundred (sheep) and the slave shall be returned to you and your son shall be flogged one-hundred stripes and be exiled for one year. And O Unais! Go in the morning to the wife of this man and ask her, and if she confesses, stone her to death." She confessed and he stoned her to death.

حَدَّثَنَا مُحَمَّدُ بْنُ يُوسُفَ، حَدَّثَنَا ابْنُ عُيَيْنَةَ، عَنِ الزُّهْرِيِّ، عَنْ عُبَيْدِ اللَّهِ بْنِ عَبْدِ اللَّهِ بْنِ عُتْبَةَ، عَنْ أَبِي هُرَيْرَةَ، وَزَيْدِ بْنِ خَالِدٍ الْجُهَنِيِّ، قَالاَ جَاءَ رَجُلٌ إِلَى النَّبِيِّ ﷺ فَقَالَ أَنْشُدُكَ اللَّهَ إِلاَّ قَضَيْتَ بَيْنَنَا بِكِتَابِ اللَّهِ. فَقَامَ خَصْمُهُ وَكَانَ أَفْقَهَ مِنْهُ فَقَالَ صَدَقَ، اقْضِ بَيْنَنَا بِكِتَابِ اللَّهِ، وَأْذَنْ لِي يَا رَسُولَ اللَّهِ. فَقَالَ النَّبِيُّ ﷺ " قُلْ ". فَقَالَ إِنَّ ابْنِي كَانَ عَسِيفًا فِي أَهْلِ، هَذَا فَزَنَى بِامْرَأَتِهِ، فَافْتَدَيْتُ مِنْهُ بِمِائَةِ شَاةٍ وَخَادِمٍ وَإِنِّي سَأَلْتُ رِجَالاً مِنْ أَهْلِ الْعِلْمِ فَأَخْبَرُونِي أَنَّ عَلَى ابْنِي جَلْدَ مِائَةٍ وَتَغْرِيبَ عَامٍ، وَأَنَّ عَلَى امْرَأَةِ هَذَا الرَّجْمَ. فَقَالَ " وَالَّذِي نَفْسِي بِيَدِهِ لأَقْضِيَنَّ بَيْنَكُمَا بِكِتَابِ اللَّهِ، الْمِائَةُ وَالْخَادِمُ رَدٌّ عَلَيْكَ، وَعَلَى ابْنِكَ جَلْدُ مِائَةٍ وَتَغْرِيبُ عَامٍ، وَيَا أُنَيْسُ اغْدُ عَلَى امْرَأَةِ هَذَا فَسَلْهَا، فَإِنِ اعْتَرَفَتْ فَارْجُمْهَا ". فَاعْتَرَفَتْ فَرَجَمَهَا.