Dó is more "to him" than just "him" - it's the 3rd person (masc.) equivalent of dom or duit. The oddness in this translation is the ligeann do construction. It would be ligim do Sheán teacht, for example, if you wanted to say I let Seán come.
(It might be helpful to remember that in English, this "let" has an implication of "give permission to", so the use of dom, duit, dó etc with lig isn't necessarily that strange).
lig do is covered in the FGB.