There are no nuances attached to the terms legitimacy (German: ehelich) or illegitimacy (unehelich). They merely define the legal status of children born in or out of wedlock. Whether we like it or not, it was (and still is) a factor in determining a child's citizenship or nationality. The concept may seem outdated, but we are dealing with events that took place nearly 100 years ago.
Under British law, my own paternal grandfather, the son of a Jewish German man and an English woman, was not legally British until his father became a naturalised British citizen in 1900.
The law in force in 1922 (Reichs- und Staatsangehörigkeitsgesetz of 1913) granted German citizenship to the children of a German father and his wife. The wife's citizenship was irrelevant. Uneheliche Kinder (illegitimate children) acquired the citizenship of the mother. This situation remained unchanged until the 1960s.
It would be very interesting to know why they did not marry, to understand the societies of Vienna and Berlin in the wake of WWI. Alexander and Marianne clearly resisted any societal pressure to marry. Maybe there were no such pressures.
According to the German version of Wikipedia, Alexander was regarded as stateless following the outbreak of WWI, and was actually interned from 1916 until the end of the war. The article goes on to say that his statelessness meant that he was unable to obtain the necessary papers to emigrate in 1938 following Germany's annexation of Austria.
So under the prevailing German law in 1922, Michael too may have been regarded as stateless if his parents had been married. Maybe this very fact explains why Alexander and Marianne did not marry.