TL;DR: We don't count $\pi$ electrons here, but the $\pi$ conjugated circuits (1). -сirculene has all conjugated circles of size $4n + 2$, and none of $2n$, what makes it an aromatic compound.
Strictly speaking, the aromaticity $4n + 2$ and antiaromaticity $4n$ rules in their original interpretation are very limited and cannot be universally applied:
According to the original Hückel $4n + 2$ rule, if a monocyclic, planar molecule has $4n + 2$ $\pi$ electrons, it is considered aromatic.
But the count of $\pi$ electrons is not what matters for polycyclic compounds, therefore a generalized $4n + 2$ rule exists: if a conjugated molecule has only $4n + 2$ $\pi$ conjugated circuits, it is considered aromatic.
Non-benzenoid compounds can have both $4n + 2$ as well as $4n$ number of conjugated circuits counted by taking into account all Kekule structures. Among non-benzenoid non-alternant polycyclic hydrocarbons -сirculene and -сirculene both have only $4n + 2$ ($6, 10, 14, ...$) numbers of circuits.
(1) Gutman, I.; Cyvin, S. J. Journal of Molecular Structure: THEOCHEM 1989, 184 (1), 159–163.
Also, check out this question regarding pyrene.