Draining problems in dishwasher. Is this drain setup ok?
Put the dishwasher drain line into the disposal. But that is NOT your air gap. There is a difference between an air gap and a trap. The output of the disposal has a trap, which is important. But you also need to have an air gap. A trap prevents sewer gas from escaping through the drain. An air gap prevents sewer water from coming into the dishwasher if the drain pipe is clogged.

However, an air gap does not need to be the old style of funny looking metal/plastic thing on the corner of the sink. Instead, you can use a flexible hose from the dishwasher that loops up above the height of the sink drain, as far as possible to the underside of the counter and then loops down and into the disposal. This does not require anything visible above the counter or any cutting holes into the sink or counter.

Assuming the corrugated plastic tube is your dishwasher drain line, move the end to the disposal and attached the middle of it as high up under the counter as you can and you're all set.