Note the differences between the stranger and the family. The dichotomy is that the stranger is alone and seeks ambition above all else. The family is together and although they entertain the stranger's notions of ambition and having "better" lives, the family is, or at least has been, quite content in their relatively simplistic lifestyle. The stranger wanders around biding his time until the opportunity for greatness will occur. Thus, he seems to have determined that settling down with a family will limit or eliminate such an opportunity. The family, on the other hand, have not concerned themselves with ambition or some legacy that will solidify their "Earthly immortality." Therefore, they might seem less idealistic in their ambition but they are certainly not lonely and have a warmth and comfort (indicated by the circle around the fire) that the stranger has not experienced. The daughter sums it up best:
"It is better to sit here, by this fire," answered the girl, blushing, "and be comfortable and contented, though nobody thinks about us."
For the stranger, the irony is that, following the tragedy, he is forgotten because he's made no long-term, significant relationships. The family has established themselves, even having had "daily converse with the world." In their quiet way, they became known for being a quaint, close-knit family. The irony is that the family, having had no ambition other than to live peacefully and happily, are remembered. ("Poets have sung their fate.") The stranger, being obsessed with ambition, is forgotten. The implication is that significant human interaction and/or relationships are more important than a selfish interest in an "Earthly immortality" or legacy.