Copying data is a fundamental operation that all computers are able to perform and it costs nothing. Therefore, data is naturally easy to copy.
Software doesn't need to be manufactured like physical goods do: the software construction step is fully automated by compilers and build systems. The cost of all this is approximately $0. Networks aren't free because of bandwidth costs, but they still make it really easy and cheap to copy data to a lot of computers.
Since games are software and software is data, it is rather easy to distribute them to an unbounded number of machines. Even if you come up with some complicated copy protection scheme, people only need to crack it once and produce a DRM-free version of the game that will work everywhere and won't do stupid things such as require an internet connection. Even cryptographically secure platforms such as the PS4 eventually got cracked and the first thing people did is enable the execution of unsigned software.
>insisting that reality should be the way that fits nicely with my arbitrary mental models
That's exactly what copyright does.