It is a nickname (or diminutive), but he's not trying to "force" anyone to use it. He just requests people call him by his nickname, just like Stanislas Wawrinka prefers 'Stan'.
Agreed. A nickname is exactly what Carlitos is to his given legal name of Carlos. As you've mentioned, nicknames are generally diminutive versions of a person's given legal name(s) or a name of reference completely different as a term of endearment or affiliation. Nothing wrong with him wanting to be called Carlitos.
Another example would be Tiger Woods. Tiger is not his given legal first name. It's the name he's known by and goes by, but it's still a nickname.
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