Yeah. The only reason I say this is because their "supported phones" link just links to the Pixel. They're not outright saying it only works on that device, but that does sort of imply it.
The headset must be device agnostic, I'd imagine, put whatever fits in there. But the Daydream software might be walled off.
Any manufacturer can produce a Daydream-ready phone; ZTE and Asus have already announced theirs. To ensure a good experience, Daydream-ready phones must meet a set of minimum standards. They need consistent performance, low motion-to-photon latency and Android N. Google don't want to harm the Daydream brand by opening it up to phones that won't provide a good VR experience.
I wouldn't expect many people to upgrade their phones purely for Daydream, but it may be a factor when their contract is up for renewal. Daydream compatibility is attractive to phone manufacturers who are struggling to differentiate their handsets or offer a compelling reason to choose a high-end device.
Edit: Clicked the link (my knowledge was from other PR) and looks like it's only for pixel