Does a Dishwasher require a Air Gap?

Yes they are required but less than half of new construction has a air gap and almost none of the older.’
Here is my report comment.

Airgaps are now standard equipment to assure a separation between
supply and waste water. It is advised that either an airgap or a high loop
be installed between the dishwasher and the waste connection

Some models have it built in but that will not be determined by you .