It’s definitely a game in the modern sense. If you want games in the traditional sense, your choices are pretty much GOG and physical copies. And even those aren’t a guarantee, with things like…
“Physical copies” that are really just download codes or a DRM key on a disc
Day one patches
Patches that make the game drastically different than it was on launch, particularly when the game was drastically different (aka. shittier) on its unpatched launch
Games that require proprietary servers to run the game properly, and won’t be kept alive after a certain date because they won’t release the required code for fans to run their own servers
For a lot of gamers, “licenses to games” or any of the above cases make up the majority of the games they play. Yet we still call them gamers, we still call them games, and we still call it gaming.