Take a piece of paper. Focus a camera on that piece of paper.
Turn on an overhead light. Did the paper change?
Now, imagine this not only to be a visual representation as limited as this, but instead causality. Then the causality sphere is, theoretically, as big as the universe itself.
The concept being discussed is the limited scope of simulation. However, it can be assumed that everything affects (or can affect) everything else. The only way to know whether or not one thing may affect anything else is to simulate it.
How could you know the sphere of causality without simulating everything?
An object's light cone is not a property of the object; it is the result of the properties of the object as they related to the light shining on that object. If the source of that light isn't represented in a simulation, then unless that object produces the light itself, the object must be dark or the simulation isn't accurate.
The discussion is about simulating a universe. Unless there are truly discrete systems within that universe, you can't do that simulation within a limited frame.
I think what the author was alluding to, though, was to say that the actual rendering of the view, rather than the calculation of the view, would be limited to the current frame of reference.
We do know the sphere of causality already, no computation needed: it is the sphere defined by the distance light has had time to travel. You don't need to simulate anything outside that zone to know that it is impossible for matter outside it to physically impact the center.
Think of it this way: if you want to simulate Earth through the year 2000, you know you don't need to simulate Alpha Centauri after 1996, since it is more than 4 light years away. You can know this without doing any computation at all.
I think you're picturing a sphere of 13Gly radius (or whatever) centred on present-day Earth, expanding at lightspeed to encompass new stars and galaxies. But while new matter enters our light-cone, it is not doing so as stars and galaxies. Those all have pasts within the light-cone - you don't need to go outside our past light-cone to find all the things that can affect them. Any matter that only entered our observable universe in the last year doesn't have a past, because it only just came through the Big Bang. It's primordial chaos, not fully-formed stars; you don't need to work out millenia of its past to know what's there. Unless for some reason the simulation needs to calculate pre-Big Bang conditions, which is possible, but then the definition of "light-cone" needs to be amended.