Is the translation for word hakam as ruler in hadith correct?

The translator has chosen ruler for word hakam. Is this correct? حَدَّثَنَا عَلِيُّ بْنُ عَبْدِ اللَّهِ، حَدَّثَنَا سُفْيَانُ، حَدَّثَنَا الزُّهْرِيُّ، قَالَ أَخْبَرَنِي سَعِيدُ بْنُ الْمُسَيَّبِ، سَمِعَ أَبَا هُرَيْرَةَ ـ رضى الله عنه ـ عَنْ رَسُولِ اللَّهِ صلى الله عليه وسلم قَالَ ‏ "‏ لاَ تَقُومُ السَّاعَةُ حَتَّى يَنْزِلَ فِيكُمُ ابْنُ مَرْيَمَ حَكَمًا مُقْسِطًا، فَيَكْسِرَ الصَّلِيبَ، وَيَقْتُلَ الْخِنْزِيرَ، وَيَضَعَ الْجِزْيَةَ، وَيَفِيضَ الْمَالُ حَتَّى لاَ يَقْبَلَهُ أَحَدٌ ‏"‏‏.‏ Narrated Abu Huraira: Allah's Messenger (ﷺ) said, "The Hour will not be established until the son of Mary (i.e. Jesus) descends amongst you as a just ruler, he will break the cross, kill the pigs, and abolish the Jizya tax. Money will be in abundance so that nobody will accept it (as charitable gifts). Sahih al-Bukhari 2476 https://sunnah.com/bukhari:2476 . Two people were arguing that jesus will lead prayer from dhuhr because he will be amir ul mumineen. Another said mahdi will continue as amir ul mumineen even after coming of eesa. Mahdi will lead fajr is unanimously accepted by all when Jesus prays first fajr during his second coming. Hence im asking does the hadith prove will jesus be amir ul mumineen?