A lot of games fall into the same categories of digital interactive art. Especially if its mostly a single player game, I may want to re-experience that game later, much like I might watch a DVD or VHS I still own from my childhood.
Of course I wouldn't expect their servers to still be running, which is why getting rid of DRM is important for the sake of archival
Keep in mind that players leave long before servers stop working. To me games are more of medium than an object and the artifacts left behind like stories, wikis, screenshots, videos and memes are of a higher importance and also easier to preserve. Let's say that you don't need to have a running Coliseum to understand how it works and it's societal implications.
Also most of what I see in games and movies are things originated or preserved long ago in books. And what games and movies do is summarize things and add action scenes and emotional filler.
I asked another poster just upthread about the software (such as Creative Cloud) case.
In any case the biggest examples would be software.
(I personally have no experience with such things because I will never use or pay for software that is provided in this way.)
I bet in a few years we'll have plenty of documented instances.