On one hand, I appreciate the way this perspective smooths out a lot of pointless argument in favor of an observable truth. On the other, I worry it falls prey to the streetlight effect. Sure, capacity to do things in an absolute sense is a useful thing to measure, but we already have lots of words for it; 'capacity to do things' is a bit wordy, but 'ability' as in 'disability' isn't too far off.
Similarly, even if we don't like the words we use to describe 'ability', why steal intelligence? We still need a word for the pretty obvious cluster of things relating generally to cognition, information crunching, and problem solving.
There are many axis on which Stephen Hawking and I differ (pre-death of course). I, for instance, can go jogging, or speak without machine assistance, or zip up my pants. Stephen Hawking could understand advanced mathematics and come up with physics breakthroughs. Am I smarter than Stephen Hawking? Are we even tied?
It seems evident that there are at least two types of ability that are at least somewhat decoupled from each other. Some tasks involve both, some tasks involve one, and some tasks involve the other. Certainly we see correlations between them, and it would be unwise to completely discount one when considering the other, but grouping them under one heading needlessly confuses the issue, especially when that heading is generally understood to refer to one of the types of ability specifically.
It seems clear that the word we use for the axis on which Stephen Hawking had me beat is 'intelligence'. Now that doesn't mean that the definition is set in stone whatsoever. If you want to use the same sequence of letters to describe a kind of fruit, you can do so. But regardless of if you give it a name or not, that axis, that real empirical grouping of ability, still exists. And while that grouping exists, and while a word is commonly used to refer to it, there is little reason to try and use that word to refer to something else except to try and transfer some of the associations with the grouping to that other thing. No matter what it confuses the issue.
Regardless, how we choose to define intelligence actually has little to do with the relevance of the body to the development of AI. Computers already have lots of ways to interact with the world, from a myriad of sensors to motors to screens. There is no problem with the statement "intelligence is highly dependent on the body", except the potential confusion that I noted above. There is, however, a problem with the statement "cognition is highly dependent on the body". The problem with that statement is that it is demonstrably false. Most of the body doesn't do any sort of informational computation except the simple control systems needed to handle the local area. Those control systems are fascinating (every joint has a little PID loop with incredibly clever ways of essentially integrating and deriving!), but hardly beyond the understanding or evaluation of AI researchers. So we shouldn't expect some secret of better AI in the body. We shouldn't expect it in the brain either, but certainly not the body.
edit: Having actually commented I now see how pointlessly long and confusing my comment is. Sorry about that, I'm having trouble actually translating my thoughts into words here.