Who is the intended audience in "My Papa's Waltz"?

The speaker in this poem addresses his father; this is established in the first line of the first stanza with the use of the personal possessive pronoun "your." 

"The whiskey on your breath   

Could make a small boy dizzy;   

But I hung on like death:   

Such waltzing was not easy."

In the subsequent stanzas, the speaker speaks of "you" (his father) and "me" (the speaker), as he recalls their roughhousing when he was a boy.  He remembers his father, who has apparently come home from a day of labor and an after-work drink, clumsily waltzing him around the kitchen. His father has the hands of a laborer, with a skinned knuckle and dirt-caked hands. He recalls his mother frowning at the ruckus they are causing and how he clung to his father's shirt as he "waltzed me off to bed."  

So while the poem addresses the father, it is, as all published poems are, intended for a broader audience to appreciate.