Electronic – the simplest way to interact with an I2C peripheral

This is probably off-topic, because the easiest way to achieve this is to use the tools already provided by your graphics card.

Mirror your display, adjust the resolution of your screen to that of the window, and pan the screen until the desired area is displayed.

If you want to be able to select an arbitrary window to be mirrored, you need to add this functionality to your window manager, which is impossible on Windows (but should be doable for most Linux window managers). If you want to do this with an app you're developing (or an open-source terminal), just use a second display.

The FT201X chip used on this module implements I2C slave mode only -- by default it does not operate as an I2C master. In other words, it is meant to be an I2C peripheral, not communicate with one.

In the datasheet, it does state that you can reconfigure the SCL and SDA pins as GPIO, which I suppose would allow you to bit-bang an I2C master implementation in software on the host, but it hardly seems like it would be worth the trouble.