I read it not as there are no routers anywhere, but that they've abstracted the problem of running the routers to their upstream hosting/colo/datacenter provide

I read it not as there are no routers anywhere, but that they've abstracted the problem of running the routers to their upstream hosting/colo/datacenter provider. Obviously there are routers and their systems are connected to somebody's ASN, or you wouldn't be able to reach them over the Internet.