What are examples of Go played on non-flat surfaces, like on a sphere?
I started writing another comment, but it got too large, so I'm putting this as an answer instead.

Your other question suggests that you're envisaging playing go on the surface of an actual sphere/torus. In particular that question mentions that you want "all nodes more or less equidistant".  Searching on the internet, I didn't find much evidence that this is how go is played on other topologies.

There are a few reasons why I doubt torus/sphere go has been played on actual spheres or tori. Firstly - who has a suitable torus lying around that they could use? Secondly - getting the stones to stay in place would be awkward, and examining the position would be even worse!

Instead I suggest that the usual* way to convert a flat board game into one on a sphere/torus/Klein bottle is by imagining that the edges are joined up.  For some diagrams of how the edges of the board should be joined see here.

I found a few references to playing tic tac toe and gomoku (5-in-a-row) on different surfaces, and one to playing go.  All of these assumed a standard square grid with the edges defined to be connected in some way.  The main differences from standard go seem to be:


Fewer corners and edges: A cylindrical board has just two edges, and a torus or Klein bottle surface game has no corners or edges.
The lack of corners and edges makes it harder to create immortal groups.


I did also come across a game of go on a cylindrical surface which was not just made of a standard board with edges connected. Each point still has four liberties, but the regions between edges are not all square:





*I'm not sure a 'usual' actually exists here, but this is at least the usual way to draw diagrams on these surfaces in mathematics.