Your question, whether it's a joke or not, is an example of how misunderstood and popularized pseudo-Freudianism and the like have degraded eros so that it is indistinguishable from genital sexual activity in which somebody has some kind of genital sexual release.
As his words suggest, all the old drunk wanted was a hug, and all the toddler wanted was a hug. Yes, there is an erotic aspect to that, but eros is not as limited in its sphere of action as tawdry modern thought thinks it is.
Love was consummated, in a manner appropriate to a toddler and a derelict. There was a giving and receiving of selves and affection.
Our Lord, or at any rate my Lord -- I wouldn't want to presume, described his suffering and dying on the cross as a consummation.
Actually, according to the ancient Greeks, there were (at least) five different kinds of love: agape (ideal or Platonic love), eros (passionate love), philia (love between friends), storge (natural affection, e.g., between parents and children), and xenia (hospitality towards strangers).
So, in fact, you are mistaken when you claim that the completely non-sexual hug exchanged between the child and the vagrant in this story had an "erotic aspect." That's because eros does indeed always have sexual connotations (though, of course, it need not always result in "release.")
On the other hand, you are quite right in pointing out that the word consummation does not refer only to the completion of marriage by sexual intercourse, but also to the completion and/or fulfillment of any plan, concept, or transaction.
Regards,