The Unsplash License is in the same spirit as the CC-0 License — the difference being that the Unsplash License does not include the right to compile photos from Unsplash to replicate a similar or competing service.
To summarize, the Unsplash License and the CC0 License:
Are both sublicensable and non-revocable
Both allow users to use photos for free, for personal and commercial purposes
Both don’t require attribution
Therefore, unless you’re attempting to create a similar or competing site to Unsplash using Unsplash photos, this change in License should not affect your use of Unsplash photos.