Based on https://www.vice.com/en_us/article/kz483y/scientists-are-dis... the idea seems to be that you encode the possible rules into a standard software framework which provides a general interface to board games; then you use MCTS as a general game-playing agent (since MCTS works on anything you can build a game tree for), and you run the MCTS agents for many long games. The games then get 'scored' for game quality: were there reversals of fortune as the search depth increased? Did sometimes the losing player early on wind up winning in the end? Did games usually end in a victory for one side? Did they go on for a reasonable length of turns, neither too long nor too short? Each set of rules gets a quality score, and the rulesets which lead to the best corpus of games are considered more likely to be close to how the original games worked.

Many popular games even today are not "high quality" in the slightest, though. (Think Monopoly)

I dunno about 'many'. Monopoly is infamous for being bad, is popular only for legacy reasons, and is rapidly fading. (My own family used to play Monopoly frequently, but I can't remember the last time we did, because the last few times we were able to play on the holidays, we were playing games like Pandemic or Settlers or Hill House or D&D...) If you look at how kids spend their time, on things like Minecraft or Fortnite, I think the overwhelming majority of them are better games than Monopoly.

I don't think the system actually exists yet. But there's a paper with more details on how they intend to do it: http://ludeme.eu/outputs/cig-ludeme-1.pdf

(Basically a GGP system using MCTS, but using its own higher level game description model instead of the standard Game Description Language.)