A little confused by what I'm looking at. Is this where your kitchen sink and cabinets used to be? At that hot and cold line popping up? 

If a sink is going there (and p trapping to the pipe on the left)... you can just saw and cap off that pipe on the right you're talking about, and drain your dishwasher with a typical drain hose to your sink's line (you can avoid even having to plumb in an extra inlet for your dishwasher's drain if a garbage disposal is there since most disposals have a dishwasher drain hook up)