Die Linke is the successor to the SED, a party that went defunct 25 years ago. It's been participating in the democratic process ever since reunification, and is part of several state as well as numerous local governments. For the most part, and certainly in terms of their actual political activity, the correct label is "social democratic" and not so much "extremist". It's anything but surprising they poll in the double digits, right-wing political spin notwithstanding.