In lieu of someone who knows what they are talking about, I'd guess the auto-rifle squad was four teams of two men under the direct command of the platoon leader. Each section could have up to two teams deployed with it (or not), giving two 'fire teams' (or whatever they chose to call them then) of 6 and a leader. The USMC seems to have a tradition of centralising its support weapons, even up to the present.
The manual appears to suggest what we would call 'task-orientated' units, with patrols being formed in response to the role required and the likely strength of the opposition. With this in mind I think the formal platoon and company structures would only exist in barracks.