Default phone is indeed part of the culprit here - to allow for non-web-UI users to have a phone, and be part of groups.
If the default phone is a physical phone aka Poly handset, they are locked into the group ring rotation.
If the default phone is a WebRTC/Softphone, they are cleared from rotation once they logout of the app.
If the default phone is a WebRTC/Softphone, with persistent WebRTC enabled, they are cleared from the rotation once they logout _and_ their persistent connection times out - even if they directly logout.
Groups are weird, Genesys wants you to use ACD instead.