Yes in relation to automated testing it is obviously focusing on the development aspect, but as a whole method there is an at least implied and sometimes explicitly emphasized correctness benefit, that doesn't just come from automated tests but from the method of driving design through testing.
In my personal opinion this claim goes too far. I think we can often explore aspects of design through code (including tests) but it can't be the main driver of design in any circumstance, nor does it by default or in general make our modules and programs more correct.
The key benefit of doing this is that we have to think of code in terms of invariants and testability. But that is just one of many, sometimes conflicting factors and there are certainly more approaches to doing this than writing automated (unit-) tests.
