It is absolutely possible to get a domination victory from your 1400 AD position, no question. You've got what looks like tech lead and near the top in production.
Run some merchant specialists in Memphis to generate either a Great Prophet or Great Merchant there. Finish off the Great Scientist in Amsterdam. Use the two of them to kick off a golden age, let that give you an anarchy-free swap into Bureaucracy and then use it to try to generate as many Great People as possible - preferably Great Merchants. Stop raising the espionage slider, no point to it. Tech Gunpowder -> Chemistry (hopefully getting Engineering in trade) -> Steel to unlock cannons then follow up with Nationalism to unlock Nationhood for drafting.
Cut back on unnecessary infrastructure - stuff like all the observatories and universities you're building. The goal is hitting a powerful attack timing as early as possible. Stuff like spending 150 hammers in Thebes on an Observatory to get an extra 2 or 3 beakers per turn won't pay off in time; better to either build wealth in the cities and get the crucially important Steel tech sooner, or build East Indiamen to carry your army and catapults/trebuchets you can upgrade to cannons when Steel arrives so you need less time after Steel but before you're ready to attack. Consider shutting down research and going 100% gold for a while after Nationhood to upgrade any pre-built catapults/trebuchets to cannons faster.
Get a big army as fast as possible (don't be afraid to run your cities down in size significantly and stack whip and draft unhappiness to do it faster). Move your Great General and that chariot to stand alone on a tile and combine them so you can upgrade the chariot to Medic III; it should travel along with your army but not fight anything. It's just there to heal units. Attack Churchill, take some of his coastal cities, vassalize him as soon as he's willing to capitulate. Tech towards Rifling at the same time. Reinforce your army with whatever new production you managed at home and sail to the other continent; judging by the tech level they're at now, if you're quick about it musket + cannon should still be perfectly viable to conquer at least one more of them. You can upgrade the muskets to rifles and get another, or potentially tech along towards State Property if things are looking dicey for continued conquest.