I think it is explained here, in the same post you linked:
6. Suppose one is “transferring merits” by sincerely saying, “May so and so receive merits from this good deed that I have done.” One could do Metta bhāvanā by saying, “May all beings be free from the suffering in the apāyā” or some version of it. In both cases, one is BROADCASTING one’s intention.
- However, just because one is doing such a “giving,” the intended recipient may not receive the benefits UNLESS the recipient has a matching mindset. It is just like the case of radio/TV, where the receiving device needs to be set to the “right frequency” to receive the signal.
As for the mechanism of how the beings can benefit from it, if i am not wrong, one way is that they can rejoice in listening to this transfer of merit, which can give them the causal eligibility for a better birth and understand the dhamma. Rejoicing in merits is also meritorious. Therefore, recalling past meritorious deeds you have done and dedicating them to other beings is also helpful. However, the recipient needs to have the right mindset. Lets say the recipient is a Preta and does not care about what you have just wished for, then the merit transfer will not be effective.
I am not exactly sure for the mechanisms of those who are trapped in a body though, eg human/ animals, it seems a bit more complicated since they cannot directly listen if they are far away, but perhaps there is someway for the message to reach them via the nāma loka.