The geology is interesting, but I'm not sure it helps much with the why (or why not) the bridge is there.
The coast in the background is made up of different types of rock, I've indicated the boundaries between them with purple lines. The area with the landslip is possibly a much softer rock (perhaps limestone?) in an area which is generally harder. If you look closely at the point I've marked with an arrow it appears the soft rock is actually being eroded from behind the harder material to the left. It is a similar kind of process which would cause the cave-like structures. The process here is one of wave action undermining the toe of the cliff causing the material above to fall and would be happening constantly.
In the foreground, the rocks are generally harder, but the 'island' does show some movement. Although it is difficult to be sure without a colour photo I've indicated the different layers (bedding planes) with red green and blue lines. This illustrates that there has been a slip along a fault shown roughly by the orange line. But that is a movement associated with a very long time period, or a very dramatic event (earthquake), so unlikely to pose much of a concern during the lifespan of the bridge.
The bridge itself is of a very simple construction and relatively low cost - the kind of thing a council would use on a public footpath to cross a stream or small river. It would also accommodate quite a lot of vertical movement at one end before becoming unsafe, so the builders would not have been particularly concerned about movement of the rock causing their hard work to be wasted.
Like ScouseBoy I did wonder about it being used for some kind of military installation. But the solidness of the walls on the right-hand side suggest to me that this wasn't something designed for use by the military or civil organisation - for them I'd expect to just see a sign saying 'keep away from the edge', or a barrier of wire or rope. Employee safety then would have been on the basis of common sense rather than having such a heavy physical barrier.
For me the construction of the walls very much suggests this is something the public have regular access to, either as tourists, or that the area to the right is inhabited.