I would not put Hitler, Trotsky and Stalin under the title "incubator of intellectual activities".
That said, it is indeed true that intellectual activities flourished in the beginning of 20s century in the Austro-Hungarian empire. (Budapest, Prague and Lemberg (now Lviv) also qualify for the surge of intellectual activities at the same time).
Your citation omits mathematics and exact sciences: Boltzmann worked in Viena, for example, and also E. Mach. There was a famous school of Logic, Vienna Circle. The so-called "Hungarian miracle" happened at the same time in Budapest. Suddenly it became a nursery of some of the future most famous physicists and mathematicians of 20s century.
(Mathematicians from Hungary: John von Neumann, Riesz brothers, Polya, Szego, Fejer, Lanczos, Erdos, Turan; physicists Wigner, Teller and Szilard.)
There was also a revival of all kinds of intellectual activities in the East of the Empire, Galicia and Bukowina (modern Western Ukraine). Franz Kafka and Karel Capek lived and worked in Prague.
All this leaves no doubt that the late Austro-Hungarian empire had some very favorable climate for intellectual activities. One can only speculate what where the exact conditions which produced this climate. This was a good example of what can be called "enlightened monarchy".
I want to emphasize only one aspect of this empire: diversity and tolerance. I hope other aspects will be analysed in other answers.
Most kinds of national, ethnic and religious discrimination were abolished. Earlier, in 19s century it transformed from Austrian Empire to Austro-Hungarian empire. Gradually many other "minorities" got equal rights (and representation).
Unlike in Russian empire, for example discrimination of Jews was abolished: many positions in science opened to the Jews. Jews even became eligible for nobility titles (von Neumanns, for example).
Ukrainians were always complaining about Russian oppression, Polish oppression,
but I have never heard or read them complaining about Austrian oppression.
(I lived in the former Austrian part of Ukraine in my childhood, when some older
people still remembered "Austrian times"). In the Russian empire, Ukrainian language was prohibited. Declared "non-existent". In Austro-Hungary, they published Ukrainian books and had a chair in Ukrainian history (in Lemberg/Lwow/Lviv University).
By the way, Germany of that time was also a very tolerant state, and this shows
in the extraordinary intellectual achievements in all areas. But Germany was much less diverse in its population.
It is true, that the empire fell as a result of the world war and of the motion for independence of various nations. But it was not really so bad as some national independence propagandists tried to claim. In most of those new independent nations,
the conditions for minorities became much worse than they were in the Empire.
For example, most Hungarian mathematicians and physicists listed above had to leave in 1930s, and made their careers in the West.
Part of these careers was creation of nuclear (Szillard) and thermonuclear
(Teller from Budapest and Ulam from Lwow) bombs, to mention the things best known to the general pubic.