"Late game" unit flooding is controlled by 2 mechanisms which may or may not apply depending on what you mean by late game. If by late game you mean when your empire is up to speed, ahead on techs or some other hegemony then no, the AI can have lots and lots of units flying around. If late game refers to late Eras such as Modern/Info/Future eras, then the throttles can apply.
First, if you have 12 Uranium, then you can only build a total of 12 Nukes, nuclear plants and GDRs combined (if one dies, then you can build a new one). Same with Oil for tanks and bombers or Aluminum. Second, unit maintenance is insane: some exponential thing where the number of turns and/or number of units make it very costly if/when you want to play in later eras. Technically, the 1 unit per tile also limits the number of units it is practical to build.
Early in the game the cost per unit is low, the later it gets the more it increases. In part, I dont mind this as a Stealth Bomber should be more costly to maintain than a worker. I do object to the amount it increases though (20+ per unit per turn). This can be modded to be flatter (very easy), but make it too flat and you can get unit spam (which might be the case in the pic you describe).
One other remedy is to commandeer resources like Aluminum and Uranium thru conquest and sucking up to CSs that have those resources.
