[Raistlin]

Actually, it doesn't (follow off of the pavement that is).

If you look closely (easier to see on the opposite side of the road) there isn't a dropped curb at the point where the cycle area appears to lead to the path.

However the entrance (and exit) to the area, which leads from and to the road, has a broken line.

I would suggest that the reason for having this here is not so that it tells cyclists where they can cycle (or what route to take) but so that it reminds motorists that:

a) There may be cyclists crossing their path, and
b) Cyclists (like other traffic going across the junction) have right of way and that they must wait until the junction is clear before moving off.

You would find that if cyclists were being directed to leave the pavement at the start of the box and then rejoin it at the end the lines at either end would be solid