Dogs listed in Dogs Like Mine are other Embark dogs that share a similar breed makeup to your pup. The higher the score (100 is the highest), the closer in breed breakdown the pup is to yours. Dogs listed in Dogs Like Mine may not be related to your dog, and may not share DNA with your dog. They certainly can! But that's not what's being highlighted in this feature
Another feature, the Relatives tab, shows other Embark dogs that DO share DNA with your dog. The larger percentage of shared DNA, the closer their relationship is.