Through the same chain of transmitters Shu'ba has narrated the same tradition in which he says that the Messenger of Allah (ﷺ) said (to Sa'd):

You have adjudged according to the command of God. And once he said: you have adjudged by the decision of a king.

وَحَدَّثَنَا زُهَيْرُ بْنُ حَرْبٍ، حَدَّثَنَا عَبْدُ الرَّحْمَنِ بْنُ مَهْدِيٍّ، عَنْ شُعْبَةَ، بِهَذَا الإِسْنَادِ وَقَالَ فِي حَدِيثِهِ فَقَالَ رَسُولُ اللَّهِ صلى الله عليه وسلم ‏"‏ لَقَدْ حَكَمْتَ فِيهِمْ بِحُكْمِ اللَّهِ ‏"‏ ‏.‏ وَقَالَ مَرَّةً ‏"‏ لَقَدْ حَكَمْتَ بِحُكْمِ الْمَلِكِ ‏"‏ ‏.‏