Since the creation of coffeehouses followed the siege of Vienna, why aren’t coffee products globally described in German, rather than Italian? How did Italian become the language of coffee products?

There is a story that coffeehouses began in Vienna after the failed second siege by the Ottomans in 1683, but that's not accurate. That (already overextended) siege was abruptly abandoned due to a surprise rear attack by the Polish and German forces, and the Ottomans left a lot of luxury goods behind as they fled -- tents, animals, weapons, armor, seals, gardens, foodstuffs... the Museum of Military History in Vienna still has a lot of the non perishables.

But coffee was in Europe well before that. Coffeehouses -- as places to meet, discuss ideas, and socialize as well as drink coffee--started in the middle east and spread to Europe via the Ottomans. Markman Ellis is one good author on this topic. In his article "An Introduction to the Coffee-House" (2008) he writes:

"According to the Turkish historian Ibrahim-I Peçevi, who wrote in about 1635, the first coffee-house was opened by ‘two Men, nam’d Schems and Hekim, the one from Damascus, the other from Aleppo’ in the year 962 in the Islamic calendar (1554–1555), during the reign of Süleyman I (1520–1566)... The first coffee-house in London opened just under a century later, in 1652, by a Greek Orthodox servant called Pasqua Rosee, in St Michael’s Alley, Cornhill, in the centre of the financial district of the City of London. It was sponsored by merchants from the Levant Company, the trading house that organised and regulated trade with the Ottoman Empire. These merchants had become accustomed to drinking coffee during their extended residences in the Company ‘Factories’ in the Ottoman cities of Istanbul, Izmir and Halep (or Constantinople, Smyrna and Aleppo as they knew them)"

As this describes, war was not Europe's only relationship with the Ottoman Empire--there was a lot of trade, diplomacy, travel, and therefore cultural exchange as well.

Coffee itself came to the Arab world from Africa in the 15th century. The word for coffee is derived from an Arabic word "qahwah" that in turn refers to an originial Ethiopian source, the Kaffa region. The Turkish word for coffee, borrowed from the Arabic, is "kahve."

One comprehensive scholarly book on all this is Ralph S. Hattox's Coffee and Coffeehouses -- the full text is online. Another more recent one is Ellis's The Coffee-House: A Cultural History.

As to why Italian coffee culture and terminology is so popular internationally--they invented the espresso machine. Angelo Mondioro got the first patent in 1884, but Luigi Bezzerra and Desiderio Pavoni created the basic modern machine as we know it (if with much larger boilers), and introduced it at the 1906 Milan World's Fair, after which the technology spread around Milan and Italy but not much farther until Pier Teresio Arduino built up a manufacturing and marketing powerhouse to export machines around Europe. After WWII Achille Gaggia created the smaller less dangerous espresso machine that doles out measured single shots at high pressure. In short, Italian technology was behind the spread of espresso coffee drinks in the 20th century.