And while I'm pretty sure I can still stream a random French band with moderate success from today in thirty years, I'm not so sure if I can stream games released today then. As an enthusiast I can turn to emulation, retro systems, reverse engineering to get old games going if I own a copy. Music streaming is delivering a byte stream from storage. Game streaming is a whole different beast.
Even something like billiards, players with enough wealth to have a room with a table would do so.
Personal libraries were a commonplace shortly after the printing press, as were broadsheets and then newspapers, all of which were purchased and owned. Music was impossible to 'own' before recording technology, but ownership of musical instruments, and the ability to use them, was quite widespread.
Same with TV: as soon as it became possible to record (and hence own) broadcasts, people flocked to VCRs, and had to win a court case to retain the right to do it.
My conclusion is that some people, maybe most, do wish to own the means of entertainment, and have historically purchased said means whenever they are able.
The current concern is that the ability to own, lend, and retain access to any of it, is vanishing completely. And, specifically with server-enabled games, the ability to experience almost all of them is guaranteed to vanish in just a few years.
We had game rentals too. Either way, I would argue that the shift from rentals and subscriptions based around exchangeable physical goods, to an exclusively streamed experience is a big shift, and a big deal.
Most games and sports had traditional rules that were passed on in a folk tradition, and only around the 1800s were rules gathered and written down.