I can't tell much from the diagram - the descriptions in the parts list might help - but my guess is that Parts 7 and 8 are the components of a sprag clutch. It is sometimes called an over-running clutch or a one-way clutch: it does the same thing as a pawl but is much smoother, and has almost zero backlash.
The over-running clutch approach is not as sophisticated as a differential, because where a differential drives both drum-halves with equal torque, an over-running clutch just drives whichever drum-half is rotating more slowly (that is, the one on the inside of the turn), and requires the operator to pull the handlebars sideways with enough force to cause the drum-half on the outside of the turn to rotate faster. It is OK on a small reel-mower, but not really adequate for a ride-on.
