Capture HDMI input on PC

I have a camcorder Canon Legria HF R57 . As I am recording sports events, my plan is to make a live stream on YouTube. The camera has HDMI cable available, so technically, I can coect the device to a computer. But as the computer is also a device that can only send its screen/picture, I am stuck.

1) Is there any possibility that using this camera, I could stream live on YouTube ? 2) If possible, will there be any quality loss?