It probably uses a LOT more info than only the mouse move/mouse click. Remember, google tracking is embedded in probably 99% of websites you visit so from your ip, cookies, tracking, logged in Google profile, etc... they're able to know if you're a human or not.
Nothing as dramatic : if you don't have a strong Google footprint, it is less likely that the system will recognize you automatically as human, and you'll have to answer the picture question.
If you don't have advertising cookies set then you're either a robot or a potentially unprofitable human user from Google's point of view. Both would be best avoided.
As others have noted here, that's not the goal here and the captcha will degrade to the current ones in this case, but it highlights an interesting way for internet properties to maximize their revenue per user by only allowing users whose existing advertising footprint suggests they will contribute meaningful value to use the service in the first place.
Detecting bots is the first step to this, but detecting potentially unprofitable humans would be a natural extension.
Think of it as "remember my login on this computer". If you check the box, you sacrifice security and privacy for convenience. If you don't want to be tracked, you need to perform extra steps.
