I'm not sure what you are expecting. I'm describing the algorithm used, so yes, I used the terminology of the algorithm.

Wang tiles doesn't say anything specific about the arrangment of tiles as there are many tilesets that have the Wang Tile property.

And Diablo tiles aren't wang tiles, it would be inaccurate to describe them so. It's not to do with the shape, it's to do with connectivity. You can have a floor tile north-west of a wall tile, you can have dirt north-west of a wall, you can have floor north-west of floor, but you cannot have dirt north west of floor. Wang tiles do not permit restrictions like that.