A mesma pergunta foi feita nos fóruns do Google , com um funcionário respondendo que a conexão é por LAN (exceto em alguns casos raros), mas a autenticação é feita através dos servidores do Google.
Sua resposta completa:
To be clear, connections between your client and host are direct peer-to-peer. Although the connection setup is mediated by Google servers, once it's established Google is no longer involved (except in very rare cases where we need to fall back and use a relay server). So in cases where your client and host are on the same network, once the connection is made it's likely to perform better than one that has to traverse the public Internet.
Chrome Remote Desktop uses an entirely different kind of protocol from RDP. It uses a video feed instead of sending bitmaps or images, and includes other optimizations to make the experience much better than RDP in most instances.