but it would be nice to get a little more insight into how games can move up these charts
Itch specifically does not want people to know. The first thing some people will do, is to abuse the system. And then abuse it even more. I have seen developers that were delisted for gaming the system.
You should market your game to attract genuine players, and not people that would make your metrics look better.
That being said, the metric does include a boost for new games and some sort of running average to not display the all time popularity. And the metrics are shifted with more emphasis on newness for new & popular. Apart from that boost thingy, all this is pretty obvious, when you think about it. There is an old post of leafo somewhere where this boost was mentioned. But it was not told how much it was or how long it would be active. The takeaway was: they seem to mix up the ranking a bit, so it is not an exact metric, like number of views or any such things. Maybe there are cappings or diminishing returns, so your cta would not do much, but instead make your account look suspicous. Also, you can't compare a browser game to a download game 1:1. Or a finished game to a game that releases chapters and regularly attracks recurring players.
In between the lines, I do have the impression, that Itch values natural traffic. Whatever natural means in a world of bits. But people coming over to your game from a Youtubevideo are probably worth more than people visiting your game, because they follow you and visit the game from their feed. Or not. This is speculation. But you can bet that Itch does it's best to filter out any dubious attempts to gain popularity.