Maybe not so surprising that the dog microbiome mimics that in humans considering that dogs have been bred by and been around humans for thousands of years as an example of curated selection of genes. I think the reverse is also true that the human microbiome mimics that of dogs.
The environment including the animals, plants around us and the food we eat all influences the gut microbiome, where the couple of kilograms of bacteria in and also on us has a considerably larger pool of genes that us humans in isolation.