Holacracy® replaces single, static titles and departments with multiple, dynamic roles and circles. He's probably the "Lead Link" of the "General Company Circle", e.g. https://glassfrog.holacracy.org/circles/25
So his static job title changes from "Chief Executive Officer" to "Lead Link of General Company Circle"? Can someone else step up and replace him as Lead Link? If not, doesn't seem very dynamic.
Sounds a little bit like the theory behind some communist parties' organization. Instead of a strict hierarchy, with leadership titles like Chairman or President and such, there are functional working groups or committees ("circles") with possibly intersecting membership. Then people have functional roles in those committees. The idea being that you aren't at a certain "rank" in the organization, but rather you are doing something specific in a specific sub-group of it.
It does have the problem you mention, that the leadership in practice will often end up not very dynamic. There's no leader, but the "lead link" of some particularly important "circle" will de facto be the leader of the organization, even if their official title is only something like Secretary.
