Hard to tell what that pipe is, but it may well be a vent for the floor drain. It could also be a waste stack from upper floors. Don't see how you can get rid of it. You might be able to move it, but that will involve chopping up some concrete. Trying to connect a shower drain to the floor drain will also involve chipping out some cement. It would NOT be proper to just have shower water run on that floor and into the floor drain. The floor is not considered a waterproof barrier, the seam at the wall is not watertight, and you have no curb. You need to put a preformed pan, or a membrane, on top of the concrete. If the floor is not sloped into the drain, you need to accomplish that with a preslope mud base.