I see from the forum that getting an early religion is not normally a good idea, but in this case I think Kublai starts with Mysticism and Budism is one of his favourite religions, so I went for it.
Founding a religion, while fun, and profitable, is usually a bad idea because your beakers (and later, hammers) could go to a more useful tech choice. Religion will spread to you, that's never a worry, and if it doesn't, while one AI is spending hammers on monasteries and missionaries, you're spending on an army to take said religion for your own.
Kubai is a great leader to practice war with. My first Noble win came as Kublai (in Noble's Club III) and it was much easier than I thought it would be. I got some settlers out, claimed horses & copper, and went to work. Thinking back on that game, I can remember a lot of mistakes I made, but it was still easy. Why? I had a plan and stuck with it. It was a pangea game, which gave me one bit of tactical advantage, knowing the map type, and I planned early to be a true Khan and unleash the Golden Horde.
I had to skip a lot of what crutches I was using. Religion was a big one. Wang Kong was right next to me and his ability to tech well would nab Hinduism. Judaism went to Liz. Buddhism went to Justinian. Already, I had the proto-continent divided into three factions. Had I taken a religion, one of those factions were to be mine, and since religion spreads along trade routes, I'd be attacking my own friends while furthering alienating those distant (and more of a threat) to me.
Now on to your game, I haven't had a chance to look at the save, but going from what you typed;
1. Founding religion. Usually not totally worth it for reasons laid out many times here. Chasing religion leads worker techs undiscovered, and getting your land developed is key to a good start. A good start pays off down the line - the first 1000 years are crucial to the rest of your game.
2. Early War. Kublai is such a great warrior in the early stages of the game, because, yes, of his aggressive trait, but also for the unique unit of Mongolia, the Keshik. The Keshik has such great synergy with Kublai, almost more so than Genghis. The ability to attack cities from two tiles away is very powerful, and the mobility that a Keshik army provides is second-to-none. Being able to attack a city with 20% culture the same turn you declare war means no whipped defenders in between turns. Chariots can do this, but only if there are no hills or forests between their location and a city. Keshiks ignore terrain costs for movement.
Also, ignore the -penalty for attacking cities. Keshiks fresh out of a Ger & Barracks can have flanking II, which provides a very good chance of retreating from a battle, making them good to soften up targets. They also can easily reach Combat III which gives them excellent odds on all classical & ancient units.
With Kublai, a fast, blitzkrieg-esque war can net you a lot of territory quick. I like Kublai over Genghis for this type of war because of his Creative trait, which saves hammers on having to build monuments, and starts claiming land immediately after you capture a city, and gives cultural defense in a city faster should you need to weather a counter-attack.
Later on, cities are going to have 80%-100% cultural defense and you'll need seige (or a massive tech bonus) to take cities, but in the early game, before Longbows show up, Kublai is one of the best.
3. Victory Conditions. Score during the game is only important for
ONE victory condition: Time. (Highest score @ 2050 AD) On Noble and higher, you are not often going to win a time victory. So don't plan on it. Unless one AI gets a very lucky set of circumstances, no AI is going to win on Noble before 1950-ish. You can see what victories an AI is going for by clicking the red "fist" icon which brings up the victory screen. If an AI is going for space, you can see the status of their projects. Likewise for culture, it will identify the cities going for culture, and likewise, for all other conditions.
By the mid game, you should be able to identify what sort of victory you're going for. This is not optional - unless you just want to turn victory conditions off and play SimCivilization, you're going to continue to be frustrated when the computer wins, because they're playing to win, and you're not. It's not hard to pick a victory.
Likewise, you need to identify what victories the AI is going for? Is there a single Civ that is starting to steamroll nearby Civs? You might make it a priority to build an army able to take the monster out (and by doing so, claim their lands and possibly victory). Is there a Civ going for culture? They likely have weak defenses. Get a map, find a culture city closest to your borders and RAZE IT TO THE GROUND. You pretty much just took that AI out of the race. Is there an AI that's getting a lot of votes? This can be tricky, since playing diplomacy is tough. But, if you have a window of war, use it, get larger, and control the AP/UN from a bully pulpit.
Its easy to fall into the line of thought that you have to play as if you were that leader, but with all the advantages of a modern, enlightened viewpoint. Skipping slavery, State Property, Police State - playing nice and yet trying to maintain strength and independence. But Civ is a game, and like every game, there's a method to beat it.
Edit: Also, yes to the props to TMIT. He's been one of the big helps in getting me from playing Warlord/Chieftain to Prince/Monarch, following his posts & games are a big help.