I just viewed your game, And I gotta say there were several errors.
While your army composition was very good in itself.
There were some key factors you lost.
Number 0: Bad start. I dunno if u were afk or something, but you stood still for way to long in the beginning, and wasting that speed arrow.
Number 1: You didn’t take advantage of tempo. i.e. you weren’t aggressive enough. You had a nice raid going with your early knights, and you should have kept that going.
Number 2: Lack of production buildings. you build very little production buildings, due to building to many sheep pens. You should have gotten a few more earlier.
Number 3: You let the opponent get all the relics. This is partly why the Chinese had such a strong econ. Chinese gets 100 of each resources from a relic. Letting him stack up on 5 relics, gave him 500 of each resource per min.
And there are other things that one can be nit picky about.
But overall I think those factors were the major cause.
You don’t need to be afraid of the Barbican with knights, it barely does damage. you treated it as if it was a keep.
Opening up with archers were ok, however I would prefer to open with just a few horsemen, to make him open with spears. Then you could go for the archers. But that’s just personal preference.
But its food for thought, which the mongols are so great at.
is to lure the opponent into building the wrong counter units.
Lack of scouting in the northern flank.
If you had a few extra scouts, you could have scouted out the northern flank, realising it was pretty Vournarable.
If you attacked through the north, you would have been able to hit his production buildings alternatively his Villages that would Pop-cap him for a bit, slowing down his production. Allowing you to to eat further into his base.
In the end, you didn’t take advantage that you had superior army during the early and mid game, and was to careful with them. If you had a few extra production buildings, suffering some losses could be compensated.
Having a few more scouts always helps a lot. Alternativly towers. To allow you to get a bit better map control and oversight where he might be moving his villagerse off. China is usually greedy and always goes for the big resources, so having something allowing you to get vision over those could give you a warning and opportunity to send a few knights to raid them.