I'm a product manager and I suspect I would do pretty well in this type of interview unless the snippet is especially complicated and/or esoteric.
In that case you might be screening for people who can talk but not actually code or people who can code but might not be the best communicator.
Interestingly enough, if youre optimizing for specific outcomes, you may not need to screen out the latter.
Engineers who struggle to communicate but are productive can be extremely successful given the right environment - including having someone on the team who knows who to work with various personalities and is technical enough.
Just some rambling, but it's worth pointing out given the scarcity of engineering talent. Not everyone is going to be Paul Bucheit, ace product manager and engineer all wrapped into one.