That said, it is different to ask if we're in a simulation vs. in a computer---the word simulation makes one think of some programmer compiling some source code and executing some program: it entails agency.
But think -- until about 50 years ago we wouldn't have necessarily thought of the universe as a computer, because we didn't think of things in terms of computers until recently. My point is this conversation and its terminology is only possible because of the present state of technical evolution -- in us and in our machines.
> What is it computing? Its own history / dynamics.
Yes, agreed. On a scale smaller than the universe, we can examine evolution by natural selection as an example of an algorithm that works in a reliable, predictable way (predictable only in a statistical sense). I prefer evolution as an example of a natural algorithmic model because it's easy to express, but produces so much complexity.