"How exactly is German case law relevant here?"
German judges are the number one candidates to populate such european courts. There is now a series of decisions in Germany, notably the Siemens document generation patent, which has abolished the exclusion of software patents in DE:
"The relevant case law is the case law of the boards of appeal of the EPO"
Administrative tribunals run by patent examiners without a law degree do not produce case law.
"why should a software engineer be privileged over an electrical engineer"
Because software authors write code, and deserve freedom of expression.
The EPO invented the term "computer implemented invention" in the late nineties because they knew that the Berne Convention was already protecting "computer programs" as literary works.
Authors are spoiled from the right to benefit of the fruits of their work.
As far as I know, electrical engineers have to deal with physical forces and all that, not with a text editor.