Arguments that could be used to support this statement would focus on the way in which this moving poem is constructed mostly out of dialogue and with little description from the poet. Thus the majority of the lines could easily be lifted out of the poem to form a dialogue that could be acted. In addition, the poem itself is based on the interaction between this young couple who are struggling to cope with the loss of their first child and the home burial that they carried out. Given the revelatory nature of this poem and the way that both speak out of their pain, we could argue that "Home Burial" could definitely be called a play in verse.
However, arguments that could be used against this statement would be the way in which the sparse narrative that comes in between the dialogue nevertheless forms a vital element of the poem that cannot be denied. For example, note the way that towards the beginning of this poem, Amy lets her husband look at what she is seeing:
She let him look, sure that he wouldn't see,
Blind creature; and awhile he didn't see.
This comment from the speaker allows us to see the thoughts and motivations of Amy, the way that she believes her husband is so unobservant that he can look at the same space but not see what mesmerises her and the way that she considers him to be a "Blind creature." Such important details would be lost if we merely felt that this was a play in verse.