To be clear, the jury cleared him of murder. He pleaded guilty to manslaughter due to diminished responsibility. He will be sentenced on Thursday and will go to jail for this. The crucial question for sentencing is how much responsibility he retained.
There is no such thing as a "court psychologist". The prosecution and defence may call psychologists as expert witnesses. Two psychologists gave evidence. I would imagine one was called by the prosecution and said pretty much what you record. The psychiatrist called by the defence said that heightened anxiety, "substantially impaired his ability to understand the nature of his conduct, form a rational judgment, and impaired his ability to exercise self-control." It seems that this, coupled with their daughter's evidence that he had been behaving strangely, was enough to mean that the prosecution had not proved murder beyond reasonable doubt.