“Absent-spirited” (7) is coined from the common word absent-minded. What denotations of “spirit” are relevant here?

The speaker in Frost's poem is somebody who is deeply acquainted with loneliness. Indeed, he stipulates at the end of the poem that no matter how lonely the world around him may feel, this does not frighten him, because his own "desert places" already contain still greater degrees of loneliness.
When he uses the descriptor "absent-spirited," the speaker says that he is too much this way "to count." This means that his spirit, or soul, is not currently very present or detectable; it is not weighty enough to "count" or to be remarked. To be spirited also, has a connotation of being vibrant or energetic. The speker, in stating that he is absent-spirited, creates a suggestion with the compound adjective that he is the opposite of this in terms of his personality; his deep loneliness seems to have overtaken whatever in him was once spirited, making him empty and devoid of life, like a "desert" where nothing grows.
Our "spirit" is whatever constitutes us outside of the physical body. It encompasses our feelings, our personality, and our indefinable soul or essence. The poet, then, may be suggesting either that his spirit—or personality and heart—is absent from within himself, as if he cannot connect with it; or that, like the absent-minded, his whole spirit is always involved with itself and unable to connect with what is outside of it. Certainly, the absent-spirited person is a lonely person, his spirit absent and as curiously blank as a desert is blank—not a vibrant place where connections can grow and bear fruit.