The excerpt you provide is written in a manner that makes it seem almost like a transcription of someone speaking (rather informally). There are errors, informal abbreviations (ad= additional), run-on sentences, sentence fragments, asides, etc. It feels like one side of an ongoing, informal exchange between or among people who understand the context very well.
SO: any comment on my part must be more or less a guess, BUT, here are a couple of possibilities:
1) this is where he's got his
self-degree of self-satisfaction,
2) this is where he's got his self-degree of self-satisfaction,= she is using 'self-degree' (a speaker-created phrase) as a way of emphasizing that the king's self-satisfaction comes from his culturally reinforced belief that he exists on a plane apart from all his subjects.
I hope this is helpful. If not, you may want to post this to a wider audience of teachers on the forum.
Student or Learner