I think it's important not to say that biology is somehow 'spooky', or not governed by physical rules. We actually know the outlines of those rules pretty well - they're just complicated.

The really big difference is that biology computes at overlapping time and distance scales, simultaneously. There are biological computational processes that occur at microseconds, to millennia, from fractions of a nanometer to kilometers all happing in concert and referencing each other. In the building of our own computational tools we generally try to avoid mixing physical scales like that. The analogies to computers aren't inherently wrong, they just need to mix in a lot more complexity.