An if a tree falls on the ship of Theseus and breaks my grandfather's axe that is resting on a table damaged enough to barely stand up afterwards debate... interesting.
The universe blinking out of existence (simulation ends, big rip, monster black hole*... take your pick) would be the more sure fire way but earth being destroyed* along with every extant atari, historical records (the radio signals into space, which would presumably include code transmitted at the end of programs to reverse engineer the language from, generally fade below background noise before too great a radius, we will assume no visiting aliens either) and such could conceivably mean that the Atari 2600 would not be a thing any more in the universe (or at least the philosophical equivalent of the Hubble volume). While normally I have some time for the three deaths thing** and Thomas Carlyle great men of history approach then for these purposes I would have to argue that even if the information is not there it did once exist and that would count.
We would have the Boltzmann brain problem to contend with where an infinite universe would eventually have to have particles arrange, transmute or ping into existence in the form of an Atari 2600 (or near enough as makes no difference) which is definitely the short end of that Boltzmann brain contemplation but that is generally not a terribly interesting problem.
*we will also skip the debate over black holes and information paradox/2d imprint of information by saying big supernova, fusion bomb or something or that the information paradox is true.
**for the unfamiliar