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Not necessarily. Commander most likely in this case refers to Supreme Commander, which is a title of absolute authority over all combat forces used by some nations. In AC4, the title of the Erusian dictator is Supreme Commander.
Badass Back: The Z.O.E. Commander's FALKEN can fire missiles backwards. Truth in Television: Some of the latest AAMs, like the Python 4/5 or AA-11/R-73, have a 360-degree targetting capability.
Big Lipped Alligator Moment: In-Universe. Ace Combat 2 had the series' first two superfighters, the ADF-01 FALKEN and the XFA-27. Neither were important to the plot at all: the XFA-27 would unceremoniously become available for purchase after a certain mission in an Extra mode playthrough, and the FALKEN was an optional boss who only appeared if you shot down the other four Z.O.E. planes across the campaign and was only set apart from any other enemy by the ability to launch missiles backwards.
Heroic Mime: Only very slightly subverted - Scarface One talks, but only when requesting assistance during landings.
Soundtrack Dissonance: Some of the songs qualify, though not intentionally. It's still an arcade game through and through, but some of the mission's music sound a little too cheerful and peppy for the situation. Almost J Pop type music.
Stealth-Based Mission: Subverted in one mission, where you're supposed to stay low to avoid radar contact, but you don't fail the mission immediately if you fly too high.