Question USB C displayport, am I doing this right?

My son has a gaming laptop, as he likes to take it with him to his friend's house sometimes. It's the gigabyte G5 KD. RTX 3060 version with a 144hz display.

I have a 24.5" 170Hz 1080p monitor that was just given to me, and would like to hook it up for him for when he plays at home. My question is, the monitor runs at 144Hz on HDMI and 170Hz on Display Port.

His laptop has a HDMI out for sure, so I know he can get 144Hz on the monitor, but I'm hoping I can get 170Hz obviously. Display Port is the only way.

The computer has a "1x DisplayPort 1.4 Type-C over USB 3.2 Gen 2". It looks like a type C USB jack on the back, but it mentions it is a DisplayPort.
Do I just get one of these cables I've linked below, and I'll be able to hit 170Hz on the monitor? It sounds like a stupid question, but I just want to be sure. Never heard of this jack before.

I've ordered this cable and this is the main point of this post. Did I order the right cable for the job?
https://www.amazon.co.jp/-/en/gp/product/B089VP676H/

This is the monitor in question that was given to me:

This is what the back usb type-C D.P. port looks like (left-most jack).

gigabyte-g5-kd-020.jpg
 
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