One service which many cloud provides include in their egress fees is transferring data through their network to close to the other end. This can improve performance as the cloud provider often has a better private network than the public internet.

This service is also one that Cloudflare provides, except they don't charge for it. It sounds like what is happening here is that the cloud providers are egressing close to the end within their network directly to Cloudflare, who is then doing the more expensive work of transferring the data to close to the other end. This makes the traffic like intra-regional traffic for the cloud provider, which is often free or deeply discounted.

Peering has been in place for a long time between cloud providers. However, the cloud providers have charged their customers the same amount regardless of whether traffic is sent across transit (which they pay incrementally for) or peering (which they don’t). The Bandwidth Alliance does two things: 1) cloud providers agree to waive or substantially discount the price of bandwidth for their customers when passing over peered connections; and 2) Cloudflare hauls the traffic at no cost to customers to the nearest location where it can be passed over a peered connection. The net effect is customers’ bandwidth bills are substantially decreased and it becomes far more affordable to move data from one cloud to another.

Even with peering in place behind the scenes, cloud providers would still usually charge for egress from storage and cdn services to a provider like cloudflare.

What Cloudflare et al are doing here is utilizing the peering connections that they have already in place and not billing at the usual egress rate when traffic routes over these peering connections.