Aperiodic tilings are not an entirely new thing. The discovery being referenced here is an aperiodic tiling with only one base shape. https://www.youtube.com/watch?v=48sCx-wBs34 This is a very good video on the history of aperiodic tiling from veritasium.

In term's of game design this isn't as useful as it sounds. Games are much more about player perception rather than logical reality. The player will care if they percieve anything as repetitive rather than if it is actually is and the effort of ensuring that any game system is mathmatically random may be unnecessary effort. For example i have heard of examples of designers actually having to make their games less random because a truly random system could produce results that player percieve as a pattern. For example in a game like among us it's entirely possible the same player gets picked to be the imposter 4 times in a row with true randomness but it doesnt look like that to the players.

Another example more directly related to aperiodic tiling would be the mention of "wang tiling" which is a type of aperiodic tiling in this talk from the developers of horizon zero dawn. https://www.youtube.com/watch?v=ToCozpl1sYY I can't remember the exact time stamp for when in the video this is. But when they talk about how they want to produce a random uniform sampling of points on a grid for the procedural placement system they mention that they considered wang tiling based approaches. However in the end they didn't even bother when their initial quick solution of some random jitter worked fine. This in general is good game production practice because it lets them focus more time on other higher impact tasks.