Installing a shelf in the bathroom
The flathead of the screw needs to fit into the keyhole bracket on the shelf and we can't tell whether it would fit or not without the measurements of the bracket.

Even if you could drill the holes in the grout lines, you would probably nick or crack a tile. I would mount that shelf in the kitchen and get a bathroom shelf constructed of a PVC material and use some heavy duty two-sided tape to secure it to the wall.