Indeed it seems cavalry is not needed. Eliminated 5 AI by ~1250 AD, and invaded 3 more with 40-50 combat3+march cuirs. AIs still don't have CoL, alphabet, feudalism, engineering... Should have built a few more cuirs and just stop teching after engineering.
Edit: continued till 1305; only vikings, japan and english remain, english are almost done. I whipped some more cuirs to speed up, have around 70 now. Only very few stacks of 10+ seen so far; Japan had a 15+ stack, about half of it catapults so they could be taken out easily.
Japan is the only AI with machinery, but crossbows are no better than swordsman against cuirs.
Cavalry is ~10 turns away but I won't need it; research was funded by conquest gold.
I'm wondering if this map could be won with knights only?
Edit2: 1350 AD victory. built 80+ cuirs total, lost a quarter of them (half of which were avoidable). Killed ~600 units. Settled 10 cities myself and captured maybe 20 more from direct neighbors, to serve as buffer around my core cities and to build wealth. I think 20 was too much, maybe should have simply razed everything.
Added a screenshot of the 160 AD situation. bulbed paper, 2xedu and lib and built an academy. As for wonders I only completed Oracle (civil service) and Heroic Epic; started on National Epic but it never completed.