This isnt quite true for digital computers, in the sense that the only property which implements the algorithm is the electrical switching state... that this state depends on, eg., silicon isnt quite the same as silicon-properties the ones "doing the work".
This is part of the trouble talking about "computation" at all, which is a nearly empty term in my view.
Consider an example. A "baking a cake" algorithm can be implemented by a person or a factory, if specified correctly. In one case, the organic properties of a person appear "essential to the implementation", but they arent. But there are some algorithms which do require organic properties (eg., if we consider the behaviour of a cell wall an algorithm) to implement.
The question is in what sense are the implementation properties "doing the computational work". Any electrical system which provides switching states is "doing the work in the same way", ie., there are certain "macro-properties" which do the work, regardless of their micro-property dependencies.
I think in the case of intelligence (the brain-body, etc.) the properties "doing the computational work" arent the macro-properties of neuronal interaction. They're properties at various scales (subcelluar protein behaviours; celluar interation; neuronal communication; bodily organization; environmental driving; etc.).
In particular, i think it's the self-adapting self-organizing properties of certain organic systems that allow them to implement "the intelligence algorithm" -- this algorithm, if it can ever be specified, I do not think will be implemented only by macroscopic neurone firing -- i'd say that'll be a very minor part of its implementation. I think most of it will come from self-organization properties from the subcell to the body.