Section 6 lists the direct object pronouns which follow transitive verbs
Apologize means to "ask forgiveness". Which in portuguese is "pedir desculpas/perdão".
"Descupar/Perdoar" is "to forgive".
So the real meaning is "I do not forgive him".
Besides there is a difference of intensity between desculpar and perdoar. I think perdoar would be forgive, and desculpar some equivalent for smaller things.
The clitic pronouns (o, a, os, as) are part of formal Portuguese grammar. "Você" is a "pronome de tratamento" and isn't even mentioned in older Portuguese grammar books. Você is used by most Brazilians and by some Portuguese. Both "você and the clitics are direct object pronouns. O = you, him, it. // A = you, her, it.
Eu não o desculpo = I don't forgive him/you.
"him" comes from the O desculpo. the literal translation would be something like: "I don't him forgive". Both in spanish and portuguese the indirect object pronoun (which reflects the person receiving the action) tends to be placed before the verb, as opposed to English.
You receive it - Você o recebeu