> How hard is the jump into the realm of computer vision/AI/robotics for someone with strong skills and experience building web applications?
If you are willing to make the jump. It's possible. You have an advantage.
> Is the coding much different?
Not as much as they have marketed you to believe.
> Is a company like this employing math/theroy-heavy people to develop new types of AI or are they working higher up the stack and just need people who can pipe data around?
No. They are not making academic thesis. You'd be surprised how primitive and "basic" many of these companies are (comparing to their marketing videos, which are click/eye baits). You can definitively make a difference there.
Of course, as other comments have mentioned, these companies still need front-end, databases, backend, and you know, normal basic automation scripts like everyone else.