Funny thing about the "web application / website" controversy is that really, both sides are right. Depending on the context of conversation, an SPA both is and is not a webpage.
Some other examples of the same linguistic phenomenon:
- We have ten fingers, but thumbs aren't fingers.
- There can be a lot of cars on the road, but minivans, SUVs, and pickup trucks aren't cars.
- The kids can go play at their friend's houses, but apartments and trailers aren't houses.
- You can see the animals at the zoo, but birds aren't animals.
- You can have a meat-free diet, but fish and fowl aren't meat.
It all depends on the distinctions that are important to the particular conversation.