I think depth is about creating meaningful choices. Should I put my city here, where it gets the cattle, or there, where it gets the incense?
Precise positioning matters a great deal to defense. I had the (same) AI civ spam cities three tiles east and west of one of my border cities during BC on Deity. It became impossible to defend that city. The AI could hit every tile I had with city bombardment, leaving me to try to defend it with a lone bowman in the city. That didn't work so well.
The placement tradeoffs in this version are like deciding in Civ 4 whether to settle on a hill in an inferior resource position or in a flat area to pick up that last resource. You may not notice below Immortal if you play a quality builder strategy, because you can get a lead and keep it. Even on Immortal, you can usually just maximize productivity and let defense be a secondary concern.
Most of the complaints about depth seem to result from playing at too low a difficulty level. The difficulties don't scale well. There are a large number of imbalanced strategies that can dominate Emperor. Those approaches start to work less well on Immortal, but they still work. But no build order and gold usage strategy is going to level the playing field on Deity.
Deity forces you to play the game the way it was meant to be played. You can't maintain many cities, you can't rush up the tech tree for Medieval (getting dominant early game defense as a bonus) when playing most civs, and you have to settle the best city sites early and often before the AI does. This approach puts you way behind, and the only hope is to outgeneral the AI badly enough to level out the production disparity. That implies keeping the fighting to one adversary at a time, which in turn implies having a strong enough defense that you can choose your wars rather than having them chosen for you by the AI.
If the AIs smell blood in the water, they will all pounce. This makes sense; if one AI DoW's you, and the others think you're hopelessly outmatched, then the best response is to dogpile and try to get some of your territory before it all goes to the rival.
It looks like the winning strategy is to fight a defensive war (you need the city support - think of it as free hammers), grind down the AI's forces, build up a counterattacking force in reserve, and unleash it once the AI is hurting and out of position.
You're right that rivers are overly emphasized. The Civil Service bonus is obviously OP. It comes way too early. Biology mid-Industrial was fine. That same bonus six techs in is not.