It is a matter of perspective, but you can have a paid downloadable for a web game - or a web playable version of a paid downloadable. On the same page.
From what was hinted in community, the alogrithm boosts new games for an unknown time frame in the popularity ranking. I do not know of any hints that they do this for old games or cycle through old games to boost them again. But the intention in those hints seemed to be, to push all the games a little bit. So, maybe. Also, old games can appear in recent again, after a "major update". And if that is really only after a devlog, they should change this. Games get a little boost by the devlog alone, since it is yet another location that has a recent system and links to the game.