It's really more of a proto-agile approach! I've never done the manual first personally, though I had a boss that had been on a project run that way early in his career who always wanted to do things that way again. The idea is to skip distilling requirements into specifications, engineering documentation, and user documentation. Instead you gather requirements AS user documentation, and only work backwards from there as necessary. Sort of like skipping all the specifications to V&V activities in a traditional systems engineering approach by writing tests first in test-driven-development.
My comparison to waterfall was a reductionistic take on the specifications up-front before coding starts aspect. If comparing it to the full waterfall process then it is definitely a fresh take!