i asked my rosh hayeshiva this question, and he answered thus: It’s pashut that you don’t “lose out” by davening/learning etc for someone else. The zchus for the person you’re doing it for is that he is the motivation for you to do it and therefore he gets a share in it, for if not for him, you wouldn’t have done it at all/done it as well. Also, certain things – like tehillim – possess a specific mystical power for certain things, like refuah for a sick person, etc.
He also said that tehillim is not talmud torah but is a form of davening (because, among other reasons, talmud Torah involoves two mitzvas: knowing & ameilus, neither of which is likely to happen when one says tehillim. With the exception of Mishnayos, that has a mystical power to simply saying the words, all Torah shbaal peh is meaningless without knowing the content. (see Rambam at end of first perek of Mishnayos Avos for classification of the words that you speak out if you are just reading the words out loud))
Also, he said that learning is by far the most powerful zchus to give someone.