Disagree on Gatling Guns (and Machine Guns, and Bazookas). .
Agree with you on Machine Guns and Bazookas, agree with Gobbledegook on Gatlings. Combat strength differential between Crossbows and Gatlings is 18 to 30, a 66% increase, which is slightly higher than the average unit upgrade but comes at the cost of 1 range and losing the ability to fire over a melee line. True, their melee strength increases even more which makes them more durable, but my experience (and it seems the experience of many here) is that crossbows have one of the widest windows of effectiveness, gatlings have one of the narrowest.
Like most people here, when I first upgraded a Xbow and was so disappointed in the results, I figured, "well, I guess I'm done with archery units." However, when a CS gifted me a machine gun, I was amazed at it's effectiveness. The combat strength differential between gatlings and machine guns is 30 to 60, a full 100% increase which I think is the highest differential in the game. Their melee combat strength is also 60, so units attacking it are attacking a unit just shy of infantry strength, and they attack with impunity also just shy of infantry strength. I'm a fan of Machine Guns and Bazookas, but the Industrial Era is the Dark Ages of ranged units.
But back to the OP, when I first read the title, "Domination without Ranged Units," I figured they meant domination without using any units that can fire with impunity, which would also include siege units.
If siege units are not omitted, then it's very possible and one of the strategies that I've used a few times on Deity - just start the game turtling with a tech/infrastructure priority, and unleash hell once artillery are available.
If siege units are omitted, it's a little trickier to get it done early, but there's still several possibilities:
-Hunnic Battering Ram rush (though it would have to be on a small or tiny map; I find once the enemy has pikes in the way, it's hard to use them.)
-Seige Towers - much longer window of effectiveness. Particularly good with Burnfire's 4UC mod, but very powerful without. Typically lend their bonus to Cbows, but with the ranged restriction could be very potent with pikes
-Impi - the whole reason to play the Zulu - designed to take cities with none (or minimal) ranged support.
And the simplest way to win Dom with melee units only is...
-XCOMS - play the game as though you're going for a tech victory, get Mercantilism/Big Ben, go Autocracy for Mobilization. spam XCOMS (get a headstart by building paratroopers, very cheap upgrade) and put a spy or diplomat in every capital for vision. Drop 6 XCOMS per capital, game is won 1-2 turns later.