Three short lines, and the poem is over almost before it begins. The speaker simply observes that their dog, like other dogs, is drawn to fire hydrants. It's a small, everyday fact, the kind of thing anyone who has walked a dog will recognize at once.
What makes it work is the tone. The speaker sounds relaxed and a little amused, almost like someone making a gentle confession. The phrase "like other dogs" quietly admits that the speaker's pet isn't special or unusual, and yet the word "mine" carries a touch of affection. This is my dog, ordinary as he is. The poem never says what the attraction is, and it doesn't need to; we fill in the sniffing, the tugging on the leash, the stop on the sidewalk.
The mood is light, dry, and warm. The brevity is part of the joke: a poem that refuses to say more than it has to, much as a dog doesn't explain itself.