run compact dishwasher drain pipe into kitchen sink
The reason for the high loop or air gap in dishwasher drains when installed below the counter are because of the risk of drain water being pushed back into the dishwasher. If you have a clog in the sink and don't have that high loop, water can drain into the dishwasher and flood out your kitchen. So with a countertop dishwasher, I don't see the need for the high loop since the drain hose is already above the level of the countertop.