But that would not imply that the underlying mechanisms are computational, only that a computational description gives an adequate account

Could you elaborate what you mean by this? Our most successful computational models of various cognitive systems at different levels of organization do remarkably well at predicting brain phenomena, to the point where we can simulate increasingly large cortical structures.

I read most of Van Gelder's last article on dynamical cognitive systems before he switched to critical thinking and argument mapping research, in BBS, and I'm still not seeing why computationalism the and dynamical systems approach are incompatible. For example, Van Gelder says that a distinguishing feature of dynamical systems is it quantitative approach to states - but of course computationalism is often quantitative about states, too. Trappenberg must be confused, too, since his textbook on computational neuroscience talks several times about dynamical systems and doesn't seem to be aware that they are somehow at odds with his program of computationalism.

Naively, it looks to me like the dynamical systems approach was largely a rection to early versions of the physical symbol system hypothesis and neural networks, but if you understand computationalism in the modern sense (which often includes models of time, quantitative state information, etc.) while still describing the system in terms of information processing, then there doesn't seem to be much conflict between the two.

Even Chemero agrees:

On our view, dynamical and [computational] explanation of the same complex system get at different but related features of said system described at different levels of abstraction and with different questions in mind. We see no a priori reason to claim that either kind of explanation is more fundamental than the other.