You have to manually save them. Don't know how the app works, but on a browser, a little save button pops up at the bottom right. Yep, just like this....
Save Game
Where those 7 games came from that are in your completed games, I have no idea.
Way back when we could play rated games against the bots and those were saved just like any rated game. Since they went away, you need to manually save anything you want to keep.
Sorry about that grey highlight...
I have no record of any games played against bots in my completed games since April 8, even though I've played many since then. For that matter, I only have a total of 7 bot games played under "Completed Games." Is there something specific that triggers computer games to be saved there? I don't recall ever manually saving any of them.