Grüezi Mr Fehr
The "whole thing" definitely works, but probably not in the way you imagine. The Optoma basically replaces an HDMI cable, i.e. sends the signals at the HDMI output of the graphics card/processor graphics to an HDMI input (beamer, screen etc.). So from there yes: the graphic output of the computer is displayed.
The touch screen itself works similar to a mouse, i.e. this "input device" is usually connected to the computer via USB. So you would need an additional (USB) transmitter at the USB output of the touchscreen to send the input to a USB receiver on the PC.
Greetings, interconnexx
NB: we have the part in operation between a UPC büxe and a beamer on the ceiling. Works flawlessly.

Hello
We use this system to show presentations on beamer and on meeting room monitor. This works very well.
Everyone can plug in their PC.
I do not know how it works with touch.

Greetings
Michael