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To be a bit pedantic, that video is incorrect in its use of the term non-euclidean. The folks behind hyperrogue made few videos that show actual non-euclidean geometry: https://youtu.be/yqUv2JO2BCs?si=AutaqS5unvT7cDjw

Comparing some of the weird geometry effects in the doom video, like things sliding sideways when you move forward, I feel like it's reasonable to call this doom non-euclidean!

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Part of the problem is that Doom isn't truly 3D, it's a 2D universe with hacks to make it look 3D.

So in the final presentation, you're seeing a facsimile of a universe where the value of Pi has only changed in two out of three spatial dimensions.

This is not really true. It is true that this particular 3D environment has some limitations, but it is 3D. A video here discussing this exact topic: https://www.youtube.com/watch?v=ZYGJQqhMN1U

For a more modern take (that's kid friendly) have a look at https://store.steampowered.com/app/1256230/Hyperbolica/

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