I'd argue that "native" is much more of a state of mind than a clear delineation anyways.

Among many game developer studios, the Steamdeck is increasingly becoming the defacto low-spec hardware target. Running their game on a Steamdeck becomes a core part of the QA process, because there's a few million Steamdecks out there actively playing games, and if your game runs on a Steamdeck you basically know it'll also run on a very wide range of hardware configs.

So while the game might be targeting a different API than the standard ones exposed on Linux machines, a lot of games now are directly designing their software to make sure they run well on a Linux handheld. Meanwhile, Linux is adopting more and more features to better support this non-standard API set.

At a certain point I think we can just call Proton/WINE a 'native' API for gaming on Linux, and say that games developed with Proton/WINE in mind are native games.

Perhaps we're not at that point yet, but we might be there soon.