I took a look at the save. It's worth considering that everyone so far at least might be rushing with their plan.
It looks like clearly your only contiguous neighbor is Korea. So far. I predict someone else will land units and settle in your area before all territory is filled, but that might not matter for trade route purposes. Korea is also the only civ with a surplus luxury or resource... so far. Naissus has horses, yes. BUT,
there is no contiguous path from Naissus to your capital that does not go through Korea's territory via coasts and roads. Ulsan also might have a cultural expansion blocking off a sea square route. If I understand correctly, if you had control of horses at Naissus, you would not have access to horses in the rest of your empire, until you have the ability for units to travel over sea and/or ocean squares without sinking in all cases. In other words not until you have Magnetism or Navigation (you can check the civiliopedia on this... it says something about harbors being able to connect differently when you learn Astronomy, Magnetism, and Navigation). At the very least, I remember having access to some luxuries in my best scoring histograph game, which I think they were from Korea and/Sumeria. Carthage lay in between my empire and theirs. I went to war before I had Navigation or Magnetism. And then I no longer had access to those luxuries for a while. Once I learned Navigation or Magnetism (don't recall which it was), or I had taken norther Carthaginian cities, then I could trade for those luxuries.
And looking again the Mongols don't even know what a luxury or strategic resource is! (so far)
So basically if you want to get luxuries or resources from any AIs you will need to do one of two things:
1. Not go to war with Korea.
2. Go to war with Korea only once you have Navigation or Magnetism or at least Astronomy.
Otherwise you will miss out on all luxuries and resources you might get from the AIs, or at least those which have to travel through the western waters.
It also looks like you have a substantial amount of territory that you might still grab. So my advice, which admittedly wasn't asked for, so perhaps I speak out of turn, would be to:
1. Clear out all the barbarians while getting in as many cities as you can. If I understand correctly, barbarian camps will not spawn in any spot with a unit with attack and defense.
2. Get as much territory as you can and/or put granaries in your cities. Like I look at Ta-tu and Kazan and think that they need granaries, and then settlers. Good that you have military that you do, to clear out/protect against barbarians, but there's a balance here.
3. Build up your infrastructure of markets, courthouses where useful, markets, and libraries/universities or banks. In other words play more builder. This map especially with how much territory you can grab favors a more builder type style from my read. Also, your combined arms attack of artillery type units and offensive units. Hopefully, that's cavalry and cannons at least. And some defensive units.
4. Attack Korea only once you have a rail network up ... or even later going for mobilization/replaceable parts. Not only is there the no trade route issue before Magnetism/Navigation/Astronomy, it will also be a substantial amount of time before replacement units can get to the front to help out.
Now, I guess you might be thinking something like "but we're already in a tech hole here! And you want us to wait for war Spoonwood? How will win if we stay behind?"
Well, I do note that, by checking the wonder build screen, that no one is building The Great Library so far. You all might swap to Literature now and go for it despite already having a decent amount of research into Republic apparently. Or capture it later, though that could become a tricky issue.
Techs also cheapen in cost as more civs that you have contact with know about the tech.
Also, as a reminder, you can steal technologies by espionage missions. Oystein wrote a
study of Espionage missions a while back. If you plan on that sort of strategy, foregoing libraries and universities would make sense until the point you could become the tech leader, if you wanted to do research.
Additionally, you don't agree to supply gpt to AIs under all conditions via the trading table. You never agree to supply gpt to them if they declare war on you. One tactic used by Moonsinger, others, and myself has been the "leave or declare" trick. This works out as follows (how much the "furious" part has gotten used though, I can't tell):
1. Basically, the AI has units in your territory, so that you can tell them to "leave or declare".
2. Your military advisor tells you that are "weak" or "average" to that AI.
3. You send them gpt only in exchange for technologies and/or gold
4. You make them furious with an outrageous demand like repeating requesting a technology for free from them. Then you say "leave or declare".
5. The AI should then declare on you cancelling the gpt deal. Except the exchange of hard goods of technologies and/or gold (or maps) doesn't go back to the AI... you get to keep it!
Another trick lies in doing 1. to 4. above, except you engage in an espionage mission against that AI. Actually, you don't need their units in your territory for this. If you fail the espionage mission, they probably declare war on you, with you getting to keep those hard goods. And that seems best used against an AI who has some technology that you don't. Because if your espionage is a steal attempt, and you succeed, then you get to keep the tech.
Furthermore, if an AI supplies you a luxury or resource to you, and they can't supply it for any reason, then the AI is responsible for failing to live up to the promise of supplying you the luxury or resource under all possible moves you make and all possible moves that other AIs make. Correspondingly, don't supply an AI a luxury or resource unless you are sure as you can that you can maintain a supply of that resource for 20 turns, or else you'll hurt your trading reputation a good bit if you can't maintain control of it.
That combined with the fact that supplying gpt to AIs can be conditional, can get leveraged to your advantage in several ways. In case you want to try to figure this sort of stuff out for yourself, I'll use a spoiler tag:
And there's some other ways to catch up in technology from behind if I recall correctly.
Which would I do? I'd pick the last one. Or at the very least, since according to Soren Johnson the man who programmed civ III's AI, they tried to design the game so that players could win every game that they played, or at least understand why they lost. So, the last one, should at least remain on the table as a possibility, if other tactics fail and seem preferable. I certainly made the mistake of taking that sort of idea off the table in some solo games I played, and quit later, because I was stubbornly refusing to use such tactics when I knew about such and had used them before.
Oh, and trade routes fail if they don't go to your capital. Even if an AI can supply say wines to 95% of your empire, if it's not supplied to your capital, then it's not supplied to your empire. And well, there's only eight tiles of roads directly adjacent to your capital on any map as opposed to possibly many more at your borders. You can also build harbors if one pillages around one's capital instead of one's borders. Though, for now, those roads may make sense. It will be a while before you have a trade network up.