Here's my two cents: I used to think like you. For me, SPA's were way to "messy" to build big stuff with. At the time, I looked a little into Ember, and had tested Angular 1.
React was the first library in which I could see myself building something big. I think it's a game changer. It deals with the hard stuff for you and let you organize your code architecture whatever you like. And yes, I think it's "the future" (maybe not react itself, but the virtual dom hype it created).
You're not even bound to SPA's. People are already using the technology to build multiple page apps, with url routing and all (e.g. react-router).
And finally, usually there's a backend behind, dealing with the data. So an app is not just the frontend. There's plenty to "play with" :D
EDIT: Almos forgot to answer the real question. haha -> I think people call modern apps SPA's because you often end up serving only one HTML file, even if the app itself has multiple pages.