TL;DR: We don't count π electrons here, rather the π conjugated circuits . -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 $4n + 2$ π electrons, it is considered aromatic.
But the count of π electrons is not what matters for polycyclic compounds, therefore a generalized $4n + 2$ rule exists: if a conjugated molecule has only $4n + 2$ π 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 $4n + 2$ $(6, 10, 14, \dots)$ numbers of circuits.
Further reading: Is there any special rules for checking the aromaticity of polycyclic compounds?
- Gutman, I.; Cyvin, S. J. Conjugated Circuits in Benzenoid Hydrocarbons. J. Mol. Struct. THEOCHEM 1989, 184 (1), 159–163. DOI: 10.1016/0166-1280(89)85141-3.