You do have to log into Steam with the same account on both PCs, don't you?

Personally I find it annoying that it doesn't have a fallback whole-desktop mode, since some game launchers (eg Minecraft) interact very badly with Steam streaming, and Microsoft insist on turning RDP off on consumer editions. You can fake it by installing Notepad as a "third party game", but it's not entirely reliable.

I ended up using Nvidia+Moonlight to stream Minecraft.