Page 92 of The Plumber's Handbook:

'Certain clear water wastes (water lifts, expansion tanks, stills, serilizers, cooling jackets, sprinkler systems, drip or overflow pans, or similar devices) contain insignificant amounts of impurities. But according to the UPC, they still have to discharge through an indirect waste pipe with an air gap before they can empty into the building drainage system."

It appears that the previous owner has comandeered your wash machine stand pipe (the pipe between the valves in the box in the picture) to improperly drain landscape water (sprinkler system ^). Apparently the landscape water and the wash machine each require the use of the indrect draining standpipe. I'd run that picture past your local plumbing inspector; he may allow you an easy fix.

Thank you -- do you know what an easy fix would be if allowed?

Your pictures don't tell us the whole story, we need to see what the piping goes to towards the left. But, from the view you do provide, trace out the pipe with a hose fitting facing downward - the hose fitting is about the right size for a dishwasher drain.

My guess from afar is that the previous owner had his washing machine drain hose connected at the red arrow ... although that arrangement has potential for siphoning water out of the machine without a siphon break involved.