The web print simple mode only supports PDF documents.
Again, that whole "cloud" terminology is a bit confusing. But your can require the web print as cloud-based in a sense the docs are being upload to a remote server somewhere either on their network or in an Cloud provider, as mentioned (Azure or Amazon). There is also a mobile print app, so you could certainly regard that as a cloud-based app. I guest you instead of referring to it as "Cloud" printing you can refer to it as "Mobile" printing.