Kruge is almost certainly nobility using only onscreen information. Deep Space 9 establishes officers were of generally of noble blood when Martok was young. (see below) Further TNG's Klingon civil war demonstrates that Klingon starships are controlled by Klingon Houses.
Examining the dialog...
Valkris, Star Trek III
Qapla’ jawwI’… bangwI’ je Success, my lord … and my love.
(From https://daily-klingon.tumblr.com/post/165409996218/qapla-jawwi-bangwi-je )
Note "jaw" is "Lord" and "wI'" is "one who does" per the klingon dictionary.
Of course there is alternate information in novels but they still tend towards his nobility.
Star Trek Deep Space 9 Once More Unto The Breach
Transcription from http://www.chakoteya.net/DS9/557.htm
MARTOK: You can wound a man without ever seeing his face. When I was a boy, my family still lived in the lowlands of Ketha Province. We had very little, but it didn't matter. We were a family of warriors. Fifteen generations had served as soldiers of the Empire, but my father had higher hopes for me. He wanted his son to become an officer. It took a great deal of effort, but eventually he found someone willing to sponsor me. I passed my entrance exam on my first attempt and all that remained was final approval by the oversight council. A simple formality. My application was rejected by one member of that council. Kor.
MARTOK: Why? Kor's family descends from the Imperial Court itself. Kor is of the blood, born to rule by the divine will of Kahless! And what was I? A boy from the Ketha lowlands. He could not bear the thought of someone like me joining the elite officer ranks. And so, to my father's embarrassment and my everlasting shame, my application was denied. And with the mark of Kor on my record I could not join even as a common soldier. I spent five years as a civilian labourer aboard General ShiVang's flagship. Then, as fortune would have it, the Romulans made a foolhardy attempt to board our ship. I earned a battlefield commission. Unfortunately, my father did not live to see that glorious day. And if Kor had had his way, I would still be a civilian on that ship, cleaning the officers' mess.