This is just a guess but considering that wolf has the same eye and hair color as the king along with the royal family's connection to a wolf spirt but especially said wolf being escorted by the king's right hand man leads me to believe that is the king in wolf form. If it was just an uncommon wolf then could just hire trustworthy guards to follow and guard it, the king's right hand man should be too busy doing that much less be willing to follow and guard anyone other than the king. Also, another wild guess is I bet the king is MC's dog Jirou reincarnated too. Then again could just be coincidence or someone else knew in past life so won't know for sure until later if ever.