Do Moffs command the Imperial Navy, and how does Tarkin exercise authority if they do not?
Short answerMoffs can make requests that officers disregard at their career's peril, while Tarkin can use superior political standing to counter another Moff. That influence is distinguished from direct military command.
NotesMoffs and Grand Moffs are described here as political officials who can request naval action without occupying the military chain of command. Refusing them can still damage an officer's career, so a request carries practical force even without a direct order. The Thrawn novels supply an example: a Moff obstructs Eli Vanto's promotion until Thrawn enlists Tarkin to counter the pressure. The distinction is between authority to issue military orders and influence over the people making military decisions.