It seems like you cant use the Texture Sheet Animation module when Mesh is selected as the Renderer module’s render mode.
In other words, when I set the Renderer module’s Render Mode to Billboard, my 2x2 texture grid shows up fine.
When I select Mesh as the Render Mode however, the particles revert to displaying the whole image (all 4 images in my 2x2 texture grid)
The options for the Texture Sheet Animation are as follows:
Tiles X:2 Y:2
Animation Whole Sheet
Frame over Time 0 4
Cycles 1