Edit : I think that i found the problem.
You need to sell 1 horse at a time. If you put more than 1 horse into the deal you will never have 2 gpt for each. You need to repeat the processus each time(i.e. propose a horse to sell for 2 gpt, make the deal, rince and repeat)
I edited this particularity.
The guide insists near the end of building at least a 4th city or more after the NC. If you cannot build more cities then maybe a Xbow rush is your next step
I had interpreted the title as having three self built cities forever mostly due to the existing "four city" guide is indeed a self build ones and had glossed over the one reference to building another one later.
But that one reference may mean this is more of a "three city NC" guide; that old "four city" guide was two city NC with 2 more cities quickly after NC.
Here's what I do if there's no fourth city available due to not a good enough location at all / marginal city state locations have killed it (NOT playing Austria / Venice) :
Take advantage of not having to spend the hammers for the fourth city and only needing 3 copies of base buildings to get National Wonders built quicker.
I'm also somewhat more likely to try to build Leaning Tower when that is the case.
Have my ships explore (as normal) : With the extra task of looking for a great city spot. If I find one, then I'll send a settler / range unit pair there to claim it; worker if needed. And am likely to send a food cargo ship to it as soon as it's built.
Nope; AI won't always buy 1 horse for 2 GPT: See attached screenshot.
Edit: This is a bad test case: The turn after I hooked up the horses (unfortunately only available on my second city) my ongoing luxury deal expired and they were no longer willing to trade luxaries 1 : 1. (Mongols developed a case of land envy)
Additional edit: Persian AI who I next met was indeed willing to give 2 GPT for a single Horse.
However, at that point he valued additional horses at nothing. (Probably because he already had 2 extra horses) Note that this sort of thing is the draw back to one at a time resource deals; if the AI is one below desired quantity of resources you can often still sell up to 5 of them at normal price, but the moment they hit the desired quantity, they won't give anything for more.