Yes it can. Some natural events, for example a flood or an earthquake, can destroy parts of the rockputer. It is therefore important for it to store the various parts of itself strategically. It shouldn't put its vital parts near the coast, or a tsunami may kill it. It should store its own consciousness in a robust way, so that it can recover from an earthquake. It's probably too slow to actually see either of them coming, but it can certainly prepare itself.

Or imagine you build two rockputers, one with black stones, another with white stones, and you have rules to remove stones when both rockputers try to expand into the same territory, a bit like in the game of Go. Then one can kill the other.

Star systems interact with each other through gravity, so you could conceive of them as some kind of gargantuan atoms, capable of making complex structures, including conscious ones. Granted, there doesn't seem to be an equivalent of the other forces at that scale, so probably it wouldn't work, but you see what I mean.