The Armenians are very strong on the water currently, with a high win rate on water and hybrid maps for 1200+ -rated players. Their land performance, on the other hand, is utterly mediocre. They have a below-average win rate on most land maps, and only a few are either average or above average.
This is because their tech tree has a great deal of holes, most of which are completely ahistorical in nature, and their specialty is infantry, which is not favored in the current meta, and is another ahistorical element. They lack Plate Barding Armor, Thumb Ring, Siege Engineers, Parthian Tactics, Heavy Cavalry Archer, Paladin, Siege Ram, Siege Onager, and Bombard Cannon. This is despite the fact that Armenian heavy cavalry, siege weapons, and archers were all historically top-tier. The Armenian navy is powerful, despite Armenia proper being landlocked and Cilician Armenia being too small to have a proper navy. Essentially, the Armenian specialties are opposite what they should be.
The way to fix both the historical and balance issues is to make the Armenian navy much weaker while making the land army much stronger. This can be done by making the Armenians essentially a jack-of-all-trades civ, with good infantry, cavalry, archers, and siege, while none are particularly exceptional. The genie (no pun intended) is already out of the bottle in terms of Armenian unique units, techs, and bonuses, so it is too late for a total overhaul, but it is still possible to tweak minor attributes. This is what I would do (some of these ideas are inspired by @UpmostRook9474):
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Replace Cilician Fleet with Cilician Engineers (possible better name): Siege weapons and Dromons +1 range and deal +25% vs buildings; Mangonel-line and Dromons fire one extra projectile (no Siege Engineers still, but a superior version available one age earlier); costs 500 food, 500 gold
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Bonus for extra Galley-line and Dromon projectile removed
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Receive Thumb Ring, but the Composite Bowman fires 18% slower to compensate (therefore only affecting other archer units)
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Receive Heavy Cavalry Archer and Parthian Tactics
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Receive Plate Barding Armor
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Receive Siege Ram and Bombard Cannon
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Lose access to Heavy Demolition Ship
With these changes, the Armenians could become only average on water maps instead of utterly overpowered, and they could become balanced on land by having a wide variety of options in the late game. They would still have an infantry specialty, but the naval specialty would probably have to be removed from the civ description, probably replaced with a Monk, Archer, or Siege classification.