I can think of at least two very rare cat breeds that looks like a dog! There might be more (yes, there is one more: Puppykat!). The first is the Lykoi or werewolf cat or sometimes called the “wolf cat”. With a nickname like that you have to chose this cat as one that looks like a dog 😉
The next is the Poodle Cat. Once again the name forces me to select this extremely rare and unusual cat as a cat that looks like a dog. To be honest there is not much of a likeness 😉 — except for the fur which is Poodle-like.
For the sake of extending this page a little bit, there are some cat breeds which are said to be “dog-like”. What does this mean? It is usual refers to cats that play fetch and follow people around but this applies to any cat of any cat breed. It is an individual cat characteristic. On this website there are some examples; a traditional Persian cat living in India is a dog-like cat to his human caretaker: Rudolph. Elisa lives with a dog raised by cats and so behaves like one. The same thing can happen in reverse. Squirrels raised by cats have learnt to purr! And you have cats with squirrel tails too….there are endless variations.
Hope lives with a Maine Coon who behaves like a guard dog.
However, some breeds are talked about in these terms more than others and one of them is the Bengal cat (dog-like Bengal cat), which probably tells us that the wild cat hybrids have a tendency to more interactive (intelligent?) and therefore more like dogs (on occasion) in their interaction with people. They might be more trainable as well and so play fetch more often.
The PetMD website refers to the Manx, Burmese and Abyssinian as dog-like cats. Don’t believe it. It’s more or less made up. Anecdotal mumbo-jumbo. As stated it is about individual cats.