The EOS Utility supports video for the 6d via only the USB cable. The video you see will be the lower resolution video as displayed on the LCD screen not the high quality video captured by the sensor and recorded to the card. This may be a marketing choice by Canon or possibly a technical limitiation due to Canon's choice of a USB 2.0 (low transfer rate) rather than USB 3.0 interface.
Note that Wi-Fi video transfer is not supported. This seems like a poor design choice by Canon for a camera at this price point.
To capture video set the camera to video mode. Start the EOS Utilitily and go to LiveView. You will see what is displayed on the LCD which may include focusing boxes and other extraneous information.
12/05/2023: New firmware updates are available.
09/26/2023: New firmware updates are available.
08/18/2023: Canon EOS R5 C training series is released.
07/31/2023: New firmware updates are available.
05/18/2023: New firmware updates are available.
03/30/2023: New firmware updates are available.