I, too, did a double-take at the use of the word, but I looked it up, and it seems to be a valid usage. Various dictionaries define program merely as a "set of instructions," so, yeah, a library or framework counts as a program just as much as a separate process.
I just felt a program is such a general and high-level way to describe software... basically anything that computes...
wikipedia: " collection of instructions that performs a specific task when executed by a computer "
We can do better than describing a JS Framework/Library, than calling it a program I guess.
I used "program" because that's what we call things that automate things for us, and that's the appropriate frame for thinking about React: it automates things you could've done by hand, but why do that?