Project to a "wireless" display over Ethernet?

This topic is a little old, but I'll put this here for future questions and for people that are still curious.

Windows 10 version 1703 extended the Miracast to Miracast over Infrastructure (Ethernet).

https://docs.microsoft.com/en-us/surface-hub/miracast-over-infrastructure

So both Wireless as well as Ethernet is now supported

EDIT: The actual idea of projecting over Ethernet using Windows 10 default support is now definitely supported as seen in the above link Miracast over Infrastructure (MICE).

MS-MICE is a recent feature added into Windows 10 version 1703 to support Miracast over Ethernet. I've not seen the technology being implemented yet however, based on the specs and descriptions it does sound promising.

Regarding your question, I'm assuming this would work on newer Windows 10 against the Miracast Wi-Fi Roku device but I don't have a Roku device to test. However, in the specs, they mentioned that the source and sink could either be Ethernet or Wi-Fi, so I'm assuming it's interchangeable. (I'm assuming you're thinking of having Ethernet Windows 10 and a WiFi Roku)

As a Miracast receiver, the Surface Hub or device must be connected to your enterprise network via either Ethernet or a secure Wi-Fi connection (e.g. using either WPA2-PSK or WPA2-Enterprise security). If the Surface Hub or device is connected to an open Wi-Fi connection, Miracast over Infrastructure will disable itself.
As a Miracast source, the Windows PC or phone must be connected to the same enterprise network via Ethernet or a secure Wi-Fi connection.

Reference from MS-MICE Specification

Enabling MS-MICE

I've not tested this feature yet, but I'm following development of Lazycast, Lazycast is a casting system that is compatible with Windows 10 Miracast on RPi and other Linux systems, I've tested this on my RPi4 and my Ubuntu Tablet and it works seamlessly as I connected to them as a Wireless Display, even the keyboard and mouse input works.

Lazycast lately has been developing on the MICE support, so if you're interested in trying out MICE, Lazycast could be one source.

If your computer's hardware doesn't support WiDi then you can't cast. You will need to get a device that can, for example Chromecast (sender & receiver).

You can still stream video files over the network by using a media server like Serviio if your TV is smart enough to find your computer, but you can't mirror without Miracast/WiDi.