That is, if they transfer the games to a special site or client (center) (a program on the computer containing a list of games and running them past the browser with a built-in flash player), then you will not ban the special site or client as I understand.
There are a lot of caveats to this answer, and it depends on what player variant is involved and how old it is. It's worth pointing out that redistributing Flash Player in a third-party application requires a distribution agreement from Adobe. Distributing Flash Player without a current distribution agreement violates our EULA.
For the specific use-cases that you care about, it's super easy to check. Just set the clock on your computer ahead to Jan 13 2021 and launch it.