It actually makes a lot of sense for practical purposes. This probably looks strange to you because most introductory cryptography texts strictly segregate stream and block ciphers. The standard pedagogical style bifurcates modern symmetric encryption into one of these two categories and talks about things like synchronization, on-the-fly encryption, speed, error correction, etc. between the two.

In point of fact, there isn't as significant a difference between the two in active research and industry. Many (most?) stream ciphers actually use blocks internally. For example, Salsa (and its spiritual successor, ChaCha) both use blocks and rounds. From one legitimate perspective, a block cipher mode enabling streaming encryption is a generalization of a stream cipher.

When you develop a stream cipher without a block system internally[1], you're trying to remove the versatility of block cipher modes in exchange for (hopefully significant) improvements in speed and efficiency. This is very difficult to do while maintaining security. At the end of the day there are only so many ways to do confusion and diffusion.

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1. For example see Sosemanuk, which internally uses a linear feedback shift register and finite state machine.