While the term open-source is a bit more vague, I'd argue that the software he's developing fits squarely into the term "free" (as in speech), as the FSF defines it. The source code is available to modify and fork, even if you must pay to access it -- which is allowed while still considering it "Free". I've always wondered how the FSF thought that would work exactly, since it seems weird to have something be forkable to only a select group of people, but this makes a lot of sense; it will be open sourced to everyone after enough people pay for it.

I'd also argue that this is one of the most ethical ways to pay developers fairly for their work, even if the author wasn't able to make that much money from it. The product the developer creates is FOSS, available to everyone after some time, and they still get paid for it (bonus; they're paid by the open source community for their work, rather than from one person/corporation that dictates their salary).