A computer will need have some form of storage (like a ROM chip) to store the most basic of an OS to provide the bare-bones minimal instructions & drivers to operate as a workstation. Even a Raspberry Pi & other micro-PC's utilize SD or even microSD cards to provide just enough storage space for the OS to load into RAM.
Please be aware that workstations tend to require more RAM than normal as it would have to utilize some of it for temporary storage of files as it sends & receives files from it's "mainframe" server & performance would be considerably lower as it has to get all it's processing resources from the server. However, it does allow the hardware on the workstation side to be considerably smaller.
In a practical application at home, Valve created the Steam Link (which the device has been discontinued, but the service is still available within the Steam software to use with PC's & mobile devices) to allow you to play your PC games remotely on your TV. It does require a fairly strong computer (definitely a gaming-class system) to do all the legwork (running the game, crunching the video frames to send to the Link & pulling input from the Link), but it allow the Steam Link client hardware to be the size similar to a Roku (closer to the Roku Ultra nowadays) that you can plug in a compatible keyboard & mouse (like the Logitech K400 wireless keyboard + trackpad) or controller (like the Steam Controller or an XBox 360 / One with the compatible USB receiver or wired directly).
The Steam Link hardware itself only has enough storage space to hold its OS & some configuration files (like computer names w/ Steam & network details), but nothing more as it delegated everything else to the PC that's being used as the server.
Hope this sheds some light on the subject.