I think I (more or less) got it.
You earn achievements, or redeem achievements to earn those white points. You then boost, which essentially converts those white points into tokens.
The red points number is, apparently, the number of tokens you can still generate on a certain day. As you boost, this amount will decrease.
But, you have a limited number of boosts you can do per day (I don't know why the limit is different to everyone).
And the maximum amount you can do for each boost is 1000 white points (meaning, you convert a maximum of 1000 white points into tokens per boost).
So, ideally, you won't waste a booster until you have more than 1000 white points, otherwise you are not converting the maximum amount of tokens possible.
I just got almost 30000 points from a game I have all but one achievements (Sleepaway Camp).
Indeed, in order to appear in the recently played games, you need to play the game for 30 minutes.
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Is there an easy way that I can check the games that I have 100% achievements?