Unfortunately it's ineligible for catalogue since it's free.
There are free games in the catalog, though.
I hear they've made exceptions but that's generally not the case and doesn't seem to be an exception they wanted to make for this game.
Why not charge for it then, even if it's just a couple bucks? I'm sure most of us will be more than happy to throw whatever money you ask for at it, your game is incredible!
Yes. Please do this. Don't you want to reach more people with your creation?