In this question, you're being asked to examine how De la Mare develops the reader's interest through his use of various literary techniques as well as the supernatural and the unknown to create intrigue.
The first point to explore is the way De La Mare introduces the setting and situation. We begin in media res, in the middle of things—the unnamed, unknown traveler is "knocking on the moonlit door" at the beginning of the poem. We do not know who the traveler is or who he is hoping to find at the abandoned house. He is "perplexed and still," as are we, the reader. Note also the gothic element of the bird which "flew up out of the turret," creating an atmospheric sense of the house as home only to animals.
Next, however, the poet introduces the "host of phantom listeners." The terminology here is eerie: they are described using such an active term; they are defined by the fact that they listen to others, and yet do not respond. Their listening is so intense that the traveler actually experiences it as a "strangeness," a response to his question. The horse, too, "moved," as if even he were aware of something existing in the house.
The listeners say nothing, as their name would suggest, but the traveler still responds to them, telling him that he "kept [his] word." Again, this one-sided conversation evokes intrigue in the reader: we do not know what the traveler has promised, or to whom he has promised it. The poet leaves the whole situation open for the reader to interpret as he or she sees fit. We are left to imagine who was in the dark house before the "listeners," and what once happened there. The house itself is now described using a host of eerie and evocative terms—"shadowiness," "still," "dark," "lone"—and the traveler is the only person "left awake" in it.
Note the ending of the poem, however—the point of view here is not that of the traveler, but of the listeners. We, the reader, are left with them as they listen to the "plunging hoofs" "surging" away as the traveler leaves the woods behind once more. The suggestion here is that the listeners will remain.