>I've never understood why certain philosophers view computation as some kind of abstract symbolic manipulation

The abstraction is over the multitude of different physical ways that computation can be performed. That is the role of abstraction, to separate something from a particular means of implementation so that we can think about computation without having to fix a particular physical process.

Sure, but I don't think that's what this paper and other similar ones are saying. I agree, of course, that things like programming languages or algorithms or even logical circuit diagrams are abstractions, obviously. But they are abstract descriptions of a real physical process that happens, for example, inside a CPU - in exactly the same way that an electrical diagram is an abstract descriptio of a real physical process that happens in an electrical circuit, or a thermodynamic calculation is a description of what happens inside an engine.

But the engine, the electrical circuit, and the computation inside the CPU are objective realities. There could be many other ways to describe and characterize the same physical realities, of course, but that doesn't make them observer-dependent phenomena.