OK, lots of conflicting and confusing information here, including just plain wrong information (alternative facts anyone, haha).
Here we go:
I2S is essentially the native format of digital audio. It is the data stream which goes directly into any DAC chip internally, and consists of 4 single ended data lines: bit clock, word clock, data, and master clock. The single ended, original version, of I2S is used internally in almost every DAC in existence.
There are some manufacturers who use I2S externally to connect a digital transport and a DAC. Typically these companies use a standard put into practice by PS Audio, where the originally single ended I2S data line are converted to balanced (known as LVDS transmission) for better integrity over a long distance (in this case a long distance being anything more than a few centimeters, as single ended I2S was never meant for anything other than internal digital transfer). LVDS I2S transmission is typically carried on an HDMI cable, but it is not HDMI, or compatible with HDMI inputs and outputs, the HDMI cable is just used because it has enough data lines to work, and is an existing cable/jack standard which manufacturers can easily adopt.
An Ethernet Renderer is a digital source component which allows for Networked audio. A Renderer, will have an Ethernet input to connect to the Network, and the usual digital output(s) to connect to a DAC. These outputs might include any of the following: SPDIF, AES (which is just balanced SPDIF), USB, I2S, etc. In terms of sound quality, the reason to use an Ethernet Renderer is to get all the noisy commercial computer gear away from the vicinity of the audio system. A typical networked audio set up right look like this:
A NAS containing music files, running a server software program such as Minimserver (free) or, perhaps ROON (not free) is in, say, the basement, connected to a network router via Ethernet cabling. Then, an Ethernet cable runs to the room where the audio system is located and connects to the Renderer. Then the Renderer connects to the DAC via the typical suspects of digital audio interconnection. The set-up is then controlled via WiFi, on an app running on a tablet or phone. Examples of Ethernet renderers are the Auralic Aries, and Sonore Rendu products. Additionally, Networked audio allows for multiple endpoints: one might use this to distribute the audio to different rooms in the home, with all the music files still stored in just one place an a NAS (network attached storage) or computer server.
There are, of course, variations on these set ups. As far as ultimate sound quality goes, if we accept "perfect" implementation in every case (hypothetically), using an Ethernet Renderer as a digital source component has the potential to offer the best ever sound quality, and it also allows for easy control and access to a large music library. But, it is not easy to make a perfect implementation, as with anything in the high end, the devil is in the details.