I wonder is there a version GoL where every bit on a computer-display or LCD TV is one cell? How does it look?

Do you mean every pixel or every sub-pixel? Sub-pixel is interesting because the geometry of the grid isn't going to be the same from one screen to the other. It might also look compressed horizontally.

Conversely, it'd be cool to play it on an large empty office building.

One window = one pixel.