It's not the edge cache itself that matters; it's that many ISPs peer directly with Google.
Google Cloud can route the audio/video/keyboard packets mostly over Google's private network and then only use the public internet once it gets to your ISP (or their transit provider). This provides Google with more control over how the packet gets to the end user.
Google provides a similar service to Google Cloud customers as the "Premium Network Service Tier".
It's the challenge of edge computing datacenter design.
However, a gaming session means to have a dedicated daemon running for you somewhere. I doubt this can be deployed anywhere on the spot, but perhaps they have some amazing technology for that.
CDNs aren't helpful if every stream is unique.