In the late 80s and early 90s the USSR broke up and most of those countries embraced capitalism. Generally the idea was that communism had been discredited. Why then have the Asian communist countries (China, Vietnam) survived and actually thrived?
First of all, because none of the Asian Communist countries actually have Communist systems anymore in any meaningful sense of the word. Both European and Asian Socialist bloc countries reformed in the 80s-90s period.
What you are really asking is why Communist parties have remained in power in Asia.
A lot of is because the Asian Communist countries were less "Communist" in the first place. Whereas the Soviet Union was an industrialized command economy, China and Vietnam were agrarian countries with comparatively small industrial sectors.
What this meant is that in the USSR you needed political change to break existing power structure propping up dying and inefficient industries. Hence the need to boot out the CPs in order to achieve meaningful economic reform, whereas in Asia, it's possible to simply build more industries disconnected from planning apparatus and on market principles instead. Thus delaying the need for political reform.
There are lots of proximate factors of course (the willingness of the CCP to simply send in the tanks at Tienanmen against a potential threat while Eastern Europe allowed their protesters to get their way in 1989). But the long term cause is that economic reform without political reform was possible in Asia but not in Europe.