I guess the first question that begs to be answered is why did historians decide to call this movement modern? Modernism can be defined as a departure from traditional styles or values. So in order to understand the specificity of this movement we need to have quick look at what constituted the Viennese society towards the end of the 19th century.
Vienna was at the time one of the largest cities in Europe and the capital of the Austro-Hungarian Empire. The historical period leading up to the Wiener Moderne has been called the Gründerzeit, which can be translated to Founders' Period. It is linked to the age of industrialisation. The events to remember, and which mark the beginning and the end of this period, are the 1848 March Revolution (student demonstrations leading to the dismissal of the Chancellor by the Emperor and the appointment of liberal ministers) and the 1873 Panic (a stock exchange crash which resulted in years of economic depression).
Subsequent to this period of industrialisation, Vienna became the fourth largest city in the world.
But in terms of intellectual progress and the development of modern thought, it was lagging behind Paris and London. Vienna, whose society was marked by its conservatism, catholicism and strong hierarchical structure, was now more than ripe for an explosion of avant-gardism and modernism.