I do not understand what you wrote (language wise)
so what "why not"?
"and "so this is (a) game ... in binary"?
I use github to upload the source code, the assets ... as the game is "(free) open source".
Once every while I compile for various platforms and archive the binaries together with the assets (so unzip it and you can execute it to play the game). These archives are uploaded as "releases".
Then on my website I can link to this release (a direct download file) and github is counting downloads for me. Of course other websites upload it on their own storage, so their downloads are not counted for me. But if they simply "hotlink" to the github files... it counts.
If you intended to ask wether you can try the game - yes you can, but this or next week we release a shiny new version after almost 2 yrs of development (you can always get it from the sources and compile on your own - but it is a "dev build" then, not a stable one.
bye
Ron