In Langston Hughes' poem "Old Walt," two things strike me. The rhythm creates a "swaying" motion, something like to and fro, back and forth—it's much the same motion one might experience while sitting quietly in a row boat on a lake. This lilting movement that Hughes imbues into his verse structurally supports the poem's theme, and this is the second thing that occurs to me upon reading the poem.
Hughes describes Whitman's writing, in terms of what motivated him: this is repeatedly referenced in this small piece of verse. It is the "seeking" and the "finding" that propels Whitman forward—according to Hughes—throughout Whitman's life. And it is not a single event, but a continuous process. One could infer, then, that when Whitman sought one answer, he moved on to another question. Whether the first question led to the second question, we have no way of knowing: but his search for answers never ceased.
In Many Worlds of Poetry, by Drachler and Terris, structure like Hughes' is described, using Sir Philip Sidney's "My True Love Hath My Heart." The device Hughes uses appears to be what his called "argument," though it may not be what we first assume when we see "argument." It is not a "fight" per se, but a "back and forth."
Argument [is] an old critical term for the line of reasoning or idea-structure of [a] poem...[using] repetition or restatement of an idea viewed from various angles.
The poem's unity is helped by the grammatical symmetry of its statements and the repetition of the thesis line. But the dominant structural feature is the argument...
The "grammatical symmetry" that is referred to above is found in Hughes' "back and forth" movement, references: "seeking, found, minding, finding, finding, minding, seeking, finding." The "repetition and restatement of an idea viewed from various angles" is exactly what Hughes does in the poem.
The rhyming pattern draws our ears to the significant idea of Whitman's "seeking" and "finding," which is the central idea of the poem. With this in mind, the reader can infer that Hughes admired the structure of Whitman's reasoning while "Old Walt" investigated (seeking) and explicated (shared his findings) regarding what he had "found."