Hello Mr. Lom!
I'd like to thank you for providing as much details with us as you can, and for providing the animated GIF that shows the stutter.
I myself have had a once every second stutter in some games, while using Linux. It took me a very long time to figure out what the issue is, and as it turned out, I've had 2-different issues in one.
The first time I had this issue, it was due to my mouse polling rate being set too high for the CPU, to be able to handle. The second time I doubt with this issue, it was due to, too much strain on my Nvidia GPU.
Considering that your not dealing with this issue while in game, I am less likely to believe that the issue is due to your GPU, especially if you are using the proprietary drivers for your GPU.
Lets start with something simple, lets adjust your mouse polling rate.
CTL ALT F2 to enter terminal
Type this code into terminal and hit enter.
sudo gedit /sys/module/usbhid/parameters/mousepoll
Then change the poll rate to 500 and save the file. Then unplug your mouse, then plug it back in. See how things operate then.