A bike can travel on the right near an intersection only when it's passing traffic that is completely stopped. If traffic is moving at all, you shouldn't be on the right, you should be in the lane. If you still want to pass, pass on the left, although if there's only a single lane of traffic in each direction you should probably just ride in the lane and wait to pass until after the intersection.
I appreciate attempts to solve real problems like this, but I doubt this design will be an improvement. The most dangerous thing a cyclist can do at an intersection is blast off the sidewalk into the crosswalk. Such a cyclist is more dangerous than properly-crossing cyclists, because from motorists' perspectives he appears out of nowhere instead of simply continuing to travel in the street. He is more dangerous than pedestrians, because he's moving much faster. This new design appears to force all cyclists into that situation: traveling quickly and appearing, to motorists, out of nowhere.
Another problem with this design is it prevents large trucks from turning right.