What is causing this stuttering issue with my XPS 9560?

If updating the BIOS doesn't fix the issue, I suggest updating the Chipset and Video drivers in correct order:

How to reinstall drivers in the correct order | Dell US

Or run the Detect Drivers utility in your Dell Product Support page - XPS 9560):

Support for XPS 15 9560 | Drivers & downloads | Dell US

Dell XPS 15 9560 BIOS Version: 1.6.2 ,1.6.2 -  DEC 12, 2017

Fixes & Enhancements:

:emotion-2:

I would suggest updating the System Setup(BIOS) to see if it will make a difference. Please watch Dell video in the link below to safety installed latest BIOS version.

How to Update BIOS (Official Dell Tech Support) - YouTube

I have actually done both of those things recently while trying to fix the other issue and it's still happening.

If the latest NVidia driver were correctly installed, I suggest you check the NVIDIA website for the latest NVidia driver. Please click on link below.

Download Drivers | NVIDIA

Note: Please create a restore point before installing any driver from the NVidia website:

Create a system restore point - support.microsoft.com

I'm assuming windows 10 is on the system

Please verify nVIDIA GeForce /GTX /Quadro graphic driver (version 23.21.13.8816, A13) were correctly installed on the system. Type Device Manager onto search box, stroll down to Display Adapters and expand it. Right click NVidia driver, select Properties, driver and then check driver version.

Lastly,

Please click on link below, hopefully it will be a help to you:

XPS 9550 and 9560: Throttling CPU under sustained 100% CPU ...

EDIT:

I have the latest driver (mine is actually 4 days newer).

And are you saying that what I recorded here is also due to throttling?

Installing drivers through the windows updates to get the best game performance:

Help Your Games Run Better With Windows 10 Game Mode

Type Setting onto the [Cortana] search box, click Update & Security, select Check For Updates. If there're updates, select Restart Now. Do the process over and over until latest windows updates are installed. The Fall Creator window update is the latest.

Windows 10 Fall Creators Update & Latest Features | See ...

"mine is actually 4 days newer "

Since the system is brand new, I suggest you contact Dell Technical Support for further assistance in link below. Keep in mind, you do have 30 days (Invoice date) of software support.

Contact Information | Dell US

Or.....

Create a support request online:

How to Create a Support Request Online? | Dell US 

Keep in mind, you do have 30 days (Invoice date) of software support.