I'm just going to leave this link over here... Not saying you should click it, but... maybe you should go to it...
> Mouse dexterity testing is incredibly irritating when you're using a TrackPoint (rubber nipple mouse) :P
The clit mouse is designed to be used by touch typists. You don't have to leave the home row to use it (use your thumbs to click).
If you handle it with the index while the other fingers of that hand rest on the keyboard (so that your hand is fixed), it becomes very precise.
I do exactly what you describe - my laptop has a trackpoint and a trackpad, and I use the former because I find it more precise. However, trying to chase moving objects is very frustrating, and dragging isn't that great either.
It's been a while since I last had one, and I don't remember trying to play with it...
I used to find it completely unusable until I finally discovered the proper way to use it (probably when I started to touch type) which was quite an epiphany. I wanted to share just in case you hadn't yet discovered it.
The big difference for me was turning on pointer acceleration and pushing the sensitivity way up, to the point where just placing a finger on the stick starts the pointer moving. That way you're not actually using very much pressure, and it makes using the stick much more comfortable and intuitive.
Having a decent cap on the thing also helps: my first TrackPoint (about ten years ago) was on a third-hand laptop, and the rubber had decayed to the point where it was squishy and sticky. Not very pleasant to use :)
TrackPoint. Now I know the name. Thank you good sir, thank you. You just made my day.
Obligatory: https://xkcd.com/243/
Glad I could be of assistance ;)
What about offering the option to switch to a normal CAPTCHA for users like yourself?
On a slightly more serious note, this is awful for anyone who has mouse dexterity issues, like older or inexperienced computer users, those using assistive devices, or even people with shaky hands. It also relies in some places on culturally specific assumptions (for instance: put toppings on a pizza... I see some squiggly reddish stuff which seems like it's meant to be bacon, but in the UK bacon doesn't look anything like that!)
Good on them for trying to make the CAPTCHA experience more interesting, but this isn't quite a complete solution...