Essential Phone faced many issues during its beta testing for Android Oreo. Due to that Essential has stated that Android Oreo 8.0 is not stable and confirmed that Essential Phone will directly receive Android Oreo 8.1. Recently beta users started to receive Android Oreo 8.1 beta update.
As stated Essential has now started to rollout Android Oreo 8.1 for its smartphone. Head to settings-> About -> software update. As the update will be rolled out in Phases it will take additional couple of days to hit all devices. The info has been officially confirmed by Essential Official twitter page.