We have in the Skipper and Skeeto community for some time had some discussions about what's allowed when speedrunning one of the games.

The thing is that it's possible to skip some of the dialogs (and thus save a lot of time) in the game if you run it in two windows (simply by opening the game twice), start the game in one of the windows, save it and then continue in the other window by loading the game. It's maybe a bit simplified, but the main point is that you need two windows of the game in order to do this.

Now to my question: Do any of you know any other games that have had similar cases? It would be nice to be able to get inspired by rules (and maybe category names) of other games that has experienced something similar.

never heard of such thing being done and its kinda smart :DD dont know how would i feel about doing such a thing in runs

A lot of open world games allow a similar concept, where you make saves, quit to menu, and load back in to skip dialogue and cutscenes. I would look at any open world game, perhaps dark souls, for rules.

We have something rather similar to this in Poptropica. It serves as more of a save warp than anything else, but that sometimes allows us to skip story progression, or just a lot of doubling back. It's allowed in the main "Any%" category, but the mods will add the category that bans it if you request it.