The original context was the gifts offered to ancestors can be received if the ancestors reborn as petas. This should be read with reference to ceremony for the departed one in contemporary brahmanical tradition:
According to brahmanical tradition, after cremation ceremony (antyesthi) the departed one has a subtle body made from wind (vayu) and space element (akasha) - this condition called “preta” (departed one). Then sraddha ceremony is done by relatives of the departed (usually first son, or first male grandchild, or first son in law, etc). For first ten days (commonly, more or less depend on the caste, how he/she died, time of death, etc), the rice ball (pinda) which is considered formed the body of preta is offered the death. On eleventh day, foods is offered to the preta and ancestors which is symbolically represented by special eleven brahmanas. On the twelfth day, a ritual called sapiṇḍikaraṇa was performed to mark union of the preta with ancestor (pitr) - this is a completion of sraddha ceremony.
And if there’s no ancestor reborn as peta, according the Buddha, the gifts is still benefit for the giver himself.
Applying merit sharing here is not supported by cultural situation in the Buddha’s time. There’s no tradition of merit sharing known from contemporary religions/sects of the time. Furthermore, merit sharing is rejected by the Buddha in MN 35 when Saccaka want to share merit acquired from his joined gifts with Licchavis to the Buddha.