My understanding is that it uses EAC and Battleye, but in an "either/or" arrangement. That is, both are installed but which one is activated when you boot the game is essentially random (or driven by some logic that is not readily apparent).

Battleye also claims to have native Linux support.

But even if it didn't, it would be trivial to have a Linux version which only used (the Linux version of) EAC. Presumably Epic have enough faith in their own anticheat product to rely on it for their flagship game for a small minority of users.