Generally, peering is how we connect with network providers like ISPs. CNI is for Cloudflare customers. Technically, they're trying to accomplish the same thing. Logistically, the way they're done could be the same — through a private network interface (a piece of fiber between our network and our peer or customer's) — or could be different (e.g., we'd be more likely to connect to a peer over an Internet Exchange (IX) where we'd be more likely to connect with a customer over a cloud network exchange). We generally hadn't offered peering or any other way to directly connect to Cloudflare's network to anyone but our largest customers in the past. CNI opens up who can take advantage of this faster, more secure, more consistent path much more broadly.
It's fantastic that Cloudflare is offering this. You might want to reconsider calling it CNI, or at least clarify that CNI is just an umbrella term for PNI and/or public peering. I'm the person that handles the PNI/IX stuff and after reading the article but before reading your comment I wasn't 100% sure if CNI was something Cloudflare specific (which we wouldn't immediately adopt) or PNI/public peering at an IX (which we would).