This spot is part of the route that has potential to help people cycling avoid congested unappealing George Street in order to get to Richmond station or other parts of Richmond from the riverside. When you come up Friars Lane from the riverside you reach a junction where the traffic is one way away from central Richmond.
If you follow the one way system left around the Green you add at least 5 minutes to your journey time. You cannot turn right and take the quicker route because it is one way. You also cannot turn right up King Street to join George Street because that is also one way.
You also cannot go straight across the path on the Green as this is officially a footpath.
There is more than one possible solution here: a contraflow for cyclists on the side of the Green nearest to George Street. A cycle path alongside the footpath straight across the Green.
King Street would also benefit from a contraflow which would open up the options for cyclists - particularly when the riverside route is flooded.