Seems that Swanage is full of mystery... here's another set of steps that, seemingly, leads nowhere. I believe, though, that until a few years ago there used to be a bench amongst the flower beds, and these steps led up to access it. The benches (there were several along the side of the tennis courts) were removed by the Council as they were attracting the "wrong sort" of usage...

If you're a budding Wimbledon star, or just fancy a knockabout with friends, you can play on the Council-owned courts here for £9 per hour (per court); or considerably less for children and club members.