East Germany along with the other Eastern Bloc countries are often referred to as communist but according to Marx communism is a state without government, money, or classes. These all existed in former East Bloc countries so why are they referred to as communist?
All of the Eastern bloc countries during the Cold War were run by Communist parties, but both in state rhetoric and internal conceptualizations, they used the term socialism. As good Marxists, they felt that "communism" was something that would arrive after a period of transition, with a Marxist-Leninist political party acting as a midwife to historical development. The continued existence of sundry details like money and wages were regrettable compromises that needed to be made for this utopian future, as did the existence of the state and a party to control it. Communism's arrival in the not too distant future was something that state propaganda emphasized. Khrushchev, for example, predicted that communism would arrive by 1980 in the Soviet sphere, a concrete position that soon became the butt of jokes and something his successors backed away from* . In the GDR, the ruling SED party, an amalgamation of the Eastern zone's SPD and KPD, with the latter having a monopoly on the leadership, the state framed its existing policies as socialist. Ulbricht framed the first few years of the GDR's policies as Aufbau des Sozialismus (erection of socialism), which involved collectivization of agriculture, the creation of a planned economy and increasing production goals, and various measures that strengthened the SED's monopoly on power. In the same vein, both the Neues Ökonomisches System, which was a response to the failures of the Aufbau campaign, still stressed developing socialism via a less hierarchically-organized planned economy. Developing socialism became one of the leitmotifs of Eastern bloc state discourse in 1960s and 70s as it became clear that the planned economy could not meet the ambitious goals of Marx's communist utopia.
*Edit: even Khrushchev hedged his rhetoric in this declaration, claiming 1980s communism would be accomplished "in the main", but the final communist utopia would still have to be built by that generation and its successor.