EAC supports Linux right now, but games publishers have to choose to turn on that particular feature.
from the mouth of Sauron itself:
> Tim Sweeney @TimSweeneyEpic > Jul 15, 2019 > EAC has native Linux binaries in beta, supporting several native games in active release. This missing link is native Linux anti-cheat integration with Wine/Proton so that games running under Wine are protected. This is in the works but is a big task.