AFAICT, that wording still doesn't appear to require each passenger to carry on their own bag.
It says, "capable of being carried onboard the aircraft by one Passenger without additional assistance", but it does not say, "capable of being carried onboard the aircraft by that Passenger without additional assistance."
I think what they may be trying to prevent is folks claiming that they need to have an unticketed companion aid in boarding to manage the carryon bag or bags. Passenger is capitalized, so I'm presuming that it refers to a ticketed Passenger.
I think that even if your ticketed child is an infant in arms, you still have a pretty good case that the ticket purchase entitles you to the baggage allowance that comes with it, provided that the adults in the party can handle the bags AND the child without help. (There IS a warm body in the seat; it's not like the baby is a cello.)
Now then, that said, as someone who has been flying with young kids for a LONG time and a lot of airmiles, be wary of trying to juggle several carryons when you have a child who must be taken by the hand or pushed in a stroller though the airport. Most of the time it is very much not worth the aggravation of trying to schlep those bags AND the child through the airport. It is a lot less stressful to bite the bullet and pay for one larger checked bag so as to lighten your load in transit.