“1000x faster?” Learn to lie better

Analogue computers are indeed capable of doing a task 1000x faster than a regular computer. The difference is they do only that task, in a very specific way, and with one specific type of output. You can 3D print at home an "analogue computer" that can solve calculus equations, it can technically be faster than a CPU, but that's the only thing it can do, it's complex, and the output is a drawing on paper.

If you come up with a repeatable and precise set of mechanical movements that are analogous to the problem you want to solve, you can indeed come up with headlines like that.