You have to be more specific. What is the inside height, width, and depth of the cabinet in which the dishwasher will be installed?

That linked chart at Coast Appliances appears to have the width and depth dimensions transposed for compact built-in. Compact built-in dishwashers typically are 18" width but standard 24" depth.

I don't know why Pargo posted that chart; it has nothing to do with the OP's request. She has a shallow(er) cabinet size for which she's trying to find a dishwasher.

The OP said "I'm looking for a dishwasher that is less than 24 inches deep."

Deep / depth is a reference of front-to-back, regards to placing a dishwasher into the cabinetry. Not width (left-to-right) or height (top-to-bottom). Thus the cabinetry size/depth is insufficient for a standard 24"-deep dishwasher.

Why is that not clear?

@dadoes: "Why is that not clear?"

Of course "depth" is clear, but the OP didn't specify the width of the dishwasher and given that it's an "old kitchen", it's a good idea to measure all the dimensions of the cutout before trying to find an appliance that will fit.